Question

Let (-3,5) be a point on the terminal side of theta. Find the exact values of sin theta, secant theta, and tangent theta

Answer 1

Answer:

Cosθ = 0.5145

Sinθ = 0.8575

Secθ = 1.9436

tanθ = 1.667

Step-by-step explanation:

From the figure attached,

Point P(-3, 5) is on the terminal side and AB is the initial side of the angle PAB.

If m∠PAB = θ

AB = $\sqrt{(3)^{2}+(5)^{2}}$

     = $\sqrt{34}$

     = 5.831

Then Cosθ = $\frac{AB}{AP}$ = $\frac{3}{5.831}$

Cosθ = 0.5145

Sinθ = $\frac{PB}{AP}$

Sinθ = $\frac{5}{5.831}$

Sinθ = 0.8575

Secθ = $\frac{1}{\text{Cos}\theta}$

Secθ = $\frac{1}{0.5145}$

Secθ = 1.944

tanθ = $\frac{PB}{AB}$

tanθ = $\frac{5}{3}$

tanθ = 1.667