Trigonometry Answers

cos(15°) can be evaluated using a sum or difference trig identity. Which of the following is equivalent to cos(15°)?

csc^2(x)−cot^2(x)=

sec(x)(sec(x)−cos(x))=

Garett is attempting to verify this trig identity. He makes a mistake on one of the lines below. Which line has his first mistake?

sec(θ)−sin(θ)tan(θ)=cos(θ)

1.1cos(θ)−sin(θ)1(sin(θ)cos(θ))=cos(θ)

2. 1cos(θ)−sin(θ)cos(θ)=cos(θ)

3. 1−sin(θ)cos(θ)=cos(θ)

4. cos(θ)=cos(θ)

What determines whether cos(theta/2) is positive or negative?

A. The quadrant that theta is located in.
B. The quadrant that theta/2 is located in.
C. The quadrant that 2theta would be located in.
D. It doesn't matter

Suppose cos(theta) = -5/13 and tan<0 find sin(2theta)

Suppose tan(theta) = 4/3 and csc<0, find tan(theta/2)

Find at least one solution to the following equation: sin(x^2 −1)/ 1−sin(x^2 −1) = sin(x) + sin^2(x) + sin^3(x) + sin^4(x) +···

Two fire spotting towers are 17 km apart on an east-west line. From Tower A, a fire is seen
on a bearing of 130°. From Tower B, the same fire is spotted on a bearing of 200°. Which
tower is closest to the fire and how far is that tower from the fire? Draw a labelled diagram.