Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Use the power-reducing identities to rewrite the expression that does not contain trigonometric functions of power greater than 1. sin x (2 cos2 x - 1) = sinxcos2x Find the exact value of the product. cos 135° cos 45° = 1 2 Use sum-to-product identities to rewrite the expression as a product. cos pi/11 - cos pi/8 cos 11 cos 8 2sin 11 2sin 2 8 sin 11 8 2 19 3 sin 176 176 Use the information given about the angle ?, to find the exact value of the indicated trigonometric function. cos ? = - 5/13, ? in quadrant II Find cos 2?. cos 5 13 cos 2 2 cos 2 1 2 25 119 1 169 169 Use the information given about the angle ?, to find the exact value of the indicated trigonometric function. tan ? =7/24 , ? in quadrant III Find sin 2?. tan 7 7 24 sin and cos 24 25 25 sin 2 2sin cos 2 7 24 336 25 25 625 Use the product-to-sum identities to rewrite the expression as the sum or difference of two functions. sin 6? sin 2? sin 6 sin 2 0.5(cos8 cos 4 ) Use half-angle identities to find the exact value of the expression. sec ( - 3pi/8) 3 sec 8 1 1 1 2.6131 cos 3 cos 3 2cos 2 3 1 8 8 16 Use the information given about the angle ? to find the exact value of the indicated trigonometric function. csc ? = -square root 6, cos ? > 0 Find sin 0/2 cos ec 6 sin 1 5 tan tan 2 tan 2 tan 2 1 2 5 1 tan 2 1 tan 2 2 2 Or, tan 2 Or, tan 1 1 5 cos 1 6 6 6 2 2 2 5 tan 2 1 0 2 5 20 4 5 6 2 We will have to consider –ve value as θ is –ve. Hence, tan Hence, sin 2 2 5 6 5 6 12 2 30 0.20872 Use a double-angle identity to find the exact value of the expression. 2 tan 15 degrees/ 1- tan^(second power) 15 degree We have tan 2 tan 1 tan 2 . 2 2 Putting θ = 30, we get tan 30 Or, 2 tan15 1 tan 2 15 2 tan15 1 tan 30 2 1 tan 15 3