Find the exact value of the following under the given conditions a.cos(a-b) b.(a-b) c.tan(a-b)

Question

tan b=-9/40, 3pi/2<β<2pi

cot a=12/35, pi<β<3pi/2

sum and difference identities

Answer 1

Your first step should be to draw the triangles.

Since tan(b) is said to be 3π/2<β<2π, then angle b must be in the 4th quadrant. Remember that you should draw the angle in reference to the x-axis. And since tan=opp/adj, the endpoint for the hypotenuse is the point (40,-9). You can then use Pythagoras' Theorem to find the length of the hypotenuse.

And since cot(a) is said to be π<α<3π/2, then angle a must be in the 3rd quadrant. Follow the same process outlined for angle b, but remember that cot=adj/opp.

The good news is that your hypotenuses are nice round numbers :).

Your drawings will help you see more clearly what is being asked. Then use your trig identities and the difference identities to find the answers to (a) & (c). Then use an inverse function to find the answer to (b).