On the trig unit circle, sin (315) = sin (-45 + 360) = sin (-45) = - sin (45) Trig table gives -> #sin 315 = -sin 45 = -(sqrt2)/2# cos 315 = cos (- 45) = cos 45 We also know that sin (90 ° – A) = cos A. Therefore, cos 53 ° = sin 37 ° = 3/5 and cos 37 ° = sin 53 ° =4/5. Now, we will move on to finding the values of tan 37 ° and tan 53 °. We are aware of the fact that tan (angle) = perpendicular/ base. For angle A, perpendicular = 4 and base = 3 whereas for angle B, perpendicular= 3 and base= 4 Using the Pythagorean Theorem, we can find the hypotenuse of this triangle. 42 + 72 = hypotenuse2 hypotenuse = √65 Now, we can evaluate the sine of the angle as the opposite side divided by the hypotenuse. sinθ = 7 √65 This gives us our desired composition. sin(tan − 1(7 4)) = sinθ = 7 √65 = 7√65 65. Exercise 4.3.3. In our example of equation (1) we might begin with the expression tan2(x) + 1 tan 2 ( x) + 1. Example 4.1.1 4.1. 1: Verifying a Trigonometric Identity. To verify that equation (1) is an identity, we work with the expression tan2(x) + 1 tan 2 ( x) + 1. It can often be a good idea to write all of the trigonometric functions in terms of the cosine Find the Exact Value sin (225) sin(225) sin ( 225) Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because sine is negative in the third quadrant. −sin(45) - sin ( 45) The exact value of sin(45) sin ( 45) is √2 2 2 2. − √2 2 - 2 2. The result can be shown in On windows, the acceptable range is approximately between -9223372036854775295 to 9223372036854775295. This range may differ on other platforms. For values outside of the acceptable range, the Sin method returns the input value, rather than throwing an exception. See Also: Cos, Tan Since we know that cosecant is the reciprocal of sine, secant is the reciprocal of sine, and cotangent is the reciprocal of tangent, we can construct these functions as follows: sec A = 1 cos A = 25 24 csc A = 1 sin A = 25 7 cot A = 1 tan A = 24 7. 2qLp.

cos tan sin values