Definitions of the Trigonometric Functions in Terms of a Unit Circle If t is a real number and P — to t, then sin t cos t tan t (x, y) is a point on the unit circle that corresponds y x 0 csc t cot t x 0 0 0.

cot 1, 9. sin , cos 0 3 5T 5. 2 3 7 sec 25, ST S 10. tanT 2 , sinT 0 X. Prove the following identities. 1. cos x cot x + sin x = csc x 11. 1 2cos x tan t cot x tan x cot x 2 2. ( 1 – cos x )( 1 + cos x ) = sin2 x 12. sin T cos4 T 1 2cos2 T 3. cot T cos T cos T cot2 T 13. T T T 1 sin 1 sin (sec tan )2 4. T T T T 2cos sin 1 (sin cos)2 14. T T T ...

Unit circle quiz sin cos tan csc sec cot

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This unit circle makes it easy to find the sin, cos, tan, csc, sec, cot without doing more work than needed. For example, to find the sin of 120 degrees you find 120 degrees on the circle. Next, you look at its coordinates and the y coordinate is the sin.So the sin120 is the square root of 3 divided by 2.

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    13. Evaluate sec 335º. Round your answer to the nearest hundredth. 14. Evaluate sec 3π 2 to the nearest hundredth. The angle is given in radians. 15. Evaluate cot π 3 to the nearest hundredth. The angle is given in radians. 16. csc 135º 13.2.1: I can use sine and ocsine to determine points around a unit circle. 17. 18. Specifically for the functions sine and cosine, for any value and if we add to t we end up at the same sint cost 2π (, )x y point on the unit circle. Thus sin(tn t+⋅ =2π) sin and cos( ) costn t+ ⋅2π = for any integer n multiple of 2π. These cyclic natures of the sine and cosine functions make them periodic functions.

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    3.The tangent function tan is equal to y x = sin cos : 4.The secant function sec is equal to 1 x = 1 cos , the reciprocal of cosine. 5.The cosecant function csc is equal to 1 y = 1 sin , the reciprocal of sine. 6.The cotangent function cot is equal to x y = cos sin ;the reciprocal of tangent. 4.2.3 The six trig functions on the right triangle

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    The cosecant (csc), secant (sec), and cotangent (cot) functions are defined using reciprocals. Their domains do not include the real numbers that make the denominator zero. csc — sin 9 sec 0 — cos cote — tan (cote 0 at odd multiples off, where tan is undefined.) You can use the unit circle to evaluate the reciprocal trigonometric ... cos cot = 1 tan sin = 1 csc cos = 1 sec tan = 1 cot tan = sin cos cot = cos sin Pythagorean Identities Consider a point on the unit circle:-x 6 y P(x;y) = (cos ;sin ) which leads to triangle 1 cos sin Using the Pythagorean theorem, we see that (memorize this one): cos2 + sin2 = 1 Derive two other identities from the one we have memorized: Divide by cos2 : cos2 cos2 + sin2 cos2 = 1 cos2 ) 1 + tan2 = sec2 Divide by sin2 :

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