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Bhanzu’s editorial team, known as Team Bhanzu, is made up of experienced educators, curriculum experts, content strategists, and fact-checkers dedicated to making math simple and engaging for learners worldwide. Every article and resource is carefully researched, thoughtfully structured, and rigorously reviewed to ensure accuracy, clarity, and real-world relevance. We understand that building strong math foundations can raise questions for students and parents alike. That’s why Team Bhanzu focuses on delivering practical insights, concept-driven explanations, and trustworthy guidance-empowering learners to develop confidence, speed, and a lifelong love for mathematics.
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(20)Sin 12 Degrees: Value, Radians, And How To Find It
Sin 12 Degrees is approximately 0.2079 (to four decimal places), and the angle 12^° equals (π)/15 radians, about 0.2094. A genuine exact form exists as a nested radical, because 12^° can be built from 30^° and 18^°, but it is too clumsy for real work, so 0.2079 is the value you actually use. The angle sits in Quadrant I, so the value is positive, and sin 12^° = cos 78^°.
Sin 11pi/6: Exact Value On The Unit Circle
Sin 11pi/6 equals -1/2, which is -0.5 as a decimal. The angle (11π)/6 radians is the same as 330^°, and it lands in the fourth quadrant of the unit circle, where sine values are negative. Its reference angle is (π)/6 (that is 30^°), so the size of the value is 1/2 and the fourth quadrant makes it negative.
Sin 8 Degrees: Value, Radians & How To Find It
Sin 8 degrees is approximately 0.1392 (to four decimal places), a small positive number because 8° sits in the first quadrant. In radians, 8° is (2π)/45 ≈ 0.1396. Unlike 30°, 45°, or 60°, the angle 8° has no clean square-root form, so the honest value is the decimal, backed by the cofunction relation sin 8^° = cos 82^°.
Sin 7pi/6: Exact Value, Unit Circle & Steps
Sin 7pi/6 equals -1/2, which is -0.5000 as a decimal. The angle (7π)/6 is the same as 210^°, and it lands in the third quadrant, where sine is negative. Its reference angle is (π)/6 (that is 30^°), and sin(π)/6 = 1/2, so the third-quadrant sign flips it to -1/2.
Sin 7pi/4: Exact Value On The Unit Circle
Sin 7pi/4 equals -(√2)/2, which is the same as -1/(√2) and about -0.7071. The angle (7π)/4 radians is 315^°, it lands in the fourth quadrant, and its reference angle is (π)/4 (45^°). Sine is negative in the fourth quadrant, so the 45^° value flips its sign.
Sin 7pi/2: Value, Unit Circle & Exact Answer
Sin 7pi/2 equals -1 exactly (decimal -1.0000). The angle (7π)/2 is 630^°, which is coterminal with (3π)/2 (270^°) once you subtract one full turn of 2π, so its terminal point on the unit circle is (0, -1) and the sine, the y-coordinate, is -1.
Sin 5pi/8: Exact Value, Steps & Unit Circle
Sin 5pi/8 equals sin 112.5^°, and its exact value is (√(2+√2))/2 ≈ 0.9239. The angle (5π)/8 sits in the second quadrant, where sine is positive, so the value is a positive number just below 1. You reach it with the half-angle identity, either from cos 45^° or from cos(5π)/4.
Sin 7 Degrees: Value, Radians & Unit Circle
Sin 7 degrees equals about 0.1219 (to four decimal places), where the angle in radians is 7^° = (7π)/180 ≈ 0.1222. Unlike sin 30^° or sin 45^°, it has no neat square-root form, so the honest answer is the decimal plus the fact that sin 7^° = cos 83^°. Because 7^° lands in the first quadrant, the value is positive.
Sin 4 Degrees: Value, Unit Circle & How To Find It
Sin 4 degrees equals approximately 0.0698 (to four decimal places), a small positive number because 4^° sits early in the first quadrant. The angle in radians is 4^° = (π)/45 ≈ 0.0698 rad, and unlike 30^° or 45^° this angle has no simple surd (square-root) form, so its value comes from a series or a calculator, not a clean radical.
Sin 3 Degrees: Value, Unit Circle & Exact Form
Sin 3 degrees equals approximately 0.0523 (to four decimal places), a small positive number because 3^° is a tiny first-quadrant angle. In radians the angle is 3^° = (π)/60 ≈ 0.0524. A true exact form does exist, since 3^° can be built from 18^° - 15^°, but it is a messy nested radical, so the four-decimal value is the one you actually use.
Sec 90 Degrees: Why It Is Undefined
Sec 90 degrees is undefined. Secant is the reciprocal of cosine, and cos 90^° = 0, so sec 90^° = 1/(cos 90^°) = 1/0, which has no value. In radians the same angle is (π)/2, so sec(π)/2 is undefined too, and the secant graph shoots up to a vertical asymptote there instead of landing on a number.
Sec 30 Degrees: Exact Value, Surds And Radians
Sec 30 Degrees is the reciprocal of cosine at that angle, so its exact value is sec 30^° = 2/(√3) = (2√3)/3 ≈ 1.1547. The angle 30^° is the same as (π)/6 radians, it sits in Quadrant I, and every trigonometric value there is positive.
Sec 7pi/6 Exact Value, Unit Circle & How To Find It
Sec 7pi/6 equals -(2√3)/3, which is about -1.1547. The angle (7π)/6 is 210^°, it sits in Quadrant III where cosine is negative, and secant is the reciprocal of cosine, so sec(7π)/6 = 1/(cos(7π)/6) = 1/(-(√3)/2) = -2/(√3) = -(2√3)/3.
Sec 45 Degrees: Exact Value √2 And Steps
Sec 45 Degrees equals √2, which is about 1.4142. Secant is the reciprocal of cosine, and cos 45^° = (√2)/2, so taking the reciprocal gives sec 45^° = √2. The angle 45^° is (π)/4 radians and sits in the first quadrant, so the value is positive.
Sec 3pi/4: Exact Value and How to Find It
Sec 3pi/4 equals -√2, which is about -1.4142. The angle (3π)/4 is 135^°, it sits in Quadrant II, and secant is the reciprocal of cosine, so sec(3π)/4 = 1/(cos(3π)/4) = 1/(-(√2)/2) = -√2. The value is negative because cosine is negative in the second quadrant.
Csc pi/6: Exact Value Is 2 (Cosec 30°)
Csc pi/6 equals exactly 2, with a decimal value of 2.0000. The angle (π)/6 radians is the same as 30^°, it sits in the first quadrant where every ratio is positive, and cosecant is the reciprocal of sine, so csc(π)/6 = 1/(sin(π)/6) = 1/(1/2) = 2.
Csc pi/4: Exact Value √2 With Unit Circle
Csc pi/4 equals √2, which is about 1.4142. It is the reciprocal of sin(π)/4, and since sin(π)/4 = (√2)/2, the cosecant is 1/(√2/2) = 2/(√2) = √2. The angle (π)/4 is 45^°, it sits in Quadrant I, and every trigonometric value there is positive, so the answer carries a plus sign.
Csc pi/3: Exact Value, Cosec 60° = 2√3/3
Csc pi/3 equals 2/(√3), which rationalises to (2√3)/3 and works out to about 1.1547. The angle (π)/3 is the radian name for 60^°, it sits in the first quadrant, and cosecant is the reciprocal of sine, so csc(π)/3 = 1/(sin(π)/3) = 1/(√3/2).
Csc pi/2: Exact Value, Unit Circle, Formula
Csc pi/2 equals exactly 1, and written as a decimal that is 1.0000. Cosecant is the reciprocal of sine, and since sin(π)/2 = 1, dividing 1 by 1 leaves 1. That value is also the smallest number cosecant ever reaches on the interval from 0 to π, which makes (π)/2 a special angle worth knowing cold.
Csc pi Explained: Why Cosecant Of pi Is Undefined
Csc pi is undefined. Cosecant is the reciprocal of sine, so csc π = 1/(sin π), and since sin π = 0, that reciprocal divides by zero. In degrees the same angle is 180^°, where the point on the unit circle is (-1, 0), a spot with height zero, which is exactly why no cosecant value exists there.