Solve the equation sec(θ)=5, for 0 ≤ θ ≤ (\pi )/(2) A) 0.803 B) 0.982 C) 1.122 D) 1.369 E) 1.577

Question

Solve the equation sec(θ)=5, for 0 ≤ θ ≤
`(\pi )/(2)`

A) 0.803
B) 0.982
C) 1.122
D) 1.369
E) 1.577

Answer 1

the answer is D) 1.369.

Explanation:

To solve the equation sec(θ) = 5, we first need to recall the definition of the secant function. The secant function is defined as the reciprocal of the cosine function:

sec(θ) = 1/cos(θ)

Therefore, our equation can be rewritten as:

1/cos(θ) = 5

To solve for θ, we need to isolate the cosine function. We can do this by multiplying both sides of the equation by cos(θ):

cos(θ) = 1/5

Now, we need to find the value of θ that satisfies this equation. To find this, we can take the inverse cosine (also known as the arccos or cos^(-1)) of both sides of the equation:

θ = cos^(-1)(1/5)

Using a calculator, we can find the value of θ to be approximately 1.369.

Therefore, the answer is D) 1.369.