If cos(t)= -7/8 where pi <t< 3pi/2, find the values of the following trigonometric functions.

Question

1. cos(2t)
2. sin(2t)
3. cos(t/2)
4. sin(t/2)

Answer 1

cost=-7/8

therefore, sint=-√15/8 using the Pythagorean Theorem

now use the following trig identities and substitute the two values:

cos2t=2cos^2t-1

sin2t=2sintcost

cos(t/2)=√((1+cost)/2)

sin(t/2)=√((1-cost)/2)

Answer 2

The easiest way to do this problem is to look up arccos(-78) in the 3rd quandrant, multiply or divide that angle and then look up the trig functions for that angle.