can someone please solve number 11 Consider the angle theta

Consider the angle theta = -12 degree. Sketch the angle is standard position. Determine a angle is the internal[0 degree -360 degree]. Rewrite the angle is radian as a multiple of x. Find the reference angle 0 degree. Find the values of the six trigonometric functions of x. Convert the angle theta = -1.45 radians to degree f(x) = 3 - 2 sin pi x g(x) = 1/2 tan(x - pi/2) h(x) = -sec(x + pi) Find cos theta when tan theta = -21/20 and sin theta

Solution

11) 5sin(3pi/4)*cos(7pi/4)

Use the identity :2 sin A cos B = sin(A + B) + sin(A B)

A = 3pi/4 ; B =7pi/4

5sin(3pi/4)*cos(7pi/4) = (5/2)[ sin(3pi/4 +7pi/4) +sin(3pi/4 - 7pi4) ]

= (5/2)[ sin(5pi/2) - sin(pi) ]

= (5/2)[ sin(2pi +pi/2)]

=(5/2)[ sin(pi/2)]

= 5/2