Trigonometry Answers

Prove the following trig identities

sin 2x + cos 2x / sin x + cos x = 2cosx

2sinxcosx / cos⁴x-sin⁴x = tan2x

Solve the following equations

2sin2x-3cosx = 0

sinx + cosx =0

Solve the following in the interval [0;2 π]

sinx > √3/2

cosx > √3/2

IcosxI ≤ 1/2

Let a=cos(π/3), b=cos(1radian), c=cos(1degree), we have that

A.c a

sec (theta)=negative two over the square root of three

solve for theta

Assume f(x) = sin(x+/π4)cos(π/4) + cos(x+/π4)sin(π/4) for all x elements of R. Which of the following statements is correct?

A. f(x) = -cos(x)

B. f(x) = sin(x)

C. f(x) = cos(x)

D. f(x) = -sin(x)

Let x be an element of 0, [0, π]. We consider the inequalities {sinx>=[(2)^1/2]/2, 0<=cosx<(1/2). Which of the following statements is correct?

A. X is an element belonging to [π/4, π/3[;

B. X is an element belonging to ]π/4, 3π/4[

C. X is an element belonging to ]π/3, π]

D. X is an element belonging to ]π/3, π/2]

23.2 If f(t) = 2 sin t + 3 cost, express f(t) as a single sinusoid and hence determine its

amplitude and phase.