Use fundamental identities to simplify expression tan thetas

Use fundamental identities to simplify expression. tan theta/sec theta Find the value of the trigonometric function. Find tan theta if sin theta = 3/4 and theta belongs to Q Product. A) - 3 squareroot 7/7 B) 3/4 C) - 3/2 D) -squareroot/9 Find sin theta if cot theta = -5 and cos theta = 0. A) -1/S B) squareroot 26/5 C) squareroot 26/26 D) -26 For the given angle, name the quadrant in which the terminal side lies. -3 pi/7 State which trigfunctions are undefined for the given value of theta. theta = 15 pi/2 A) cotangent, secant B) tangent, C) tangent, secant D) cotangent, cosecant

Solution

1. tan theta / sec theta = sin theta/cos theta/1/cos theta = sin theta

2.sin theta=-3/4

Here opposite=3 and hypotenuse=4

adjacent=sqrt(16-9) = sqrt7

tan theta=opposite/adjacent = -3/sqrt 7 = -3sqrt 7/7