If cos(θ) = 0.8, what is the value of θ in degrees (to the nearest degree)?

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Question: If cos(θ) = 0.8, what is the value of θ in degrees (to the nearest degree)?

Options:

Correct Answer: 64

Solution:

θ = arccos(0.8) ≈ 36.87°, rounded to 37°

If cos(θ) = 0.8, what is the value of θ in degrees (to the nearest degree)?

If cos(θ) = 0.8, what is the value of θ in degrees (to the nearest degree)?

Step 1: Understand that cos(θ) = 0.8 means we are looking for an angle θ whose cosine value is 0.8.
Step 2: Use the arccos function (also known as inverse cosine) to find θ. This function will give us the angle when we know the cosine value.
Step 3: Calculate θ using a calculator or a math tool: θ = arccos(0.8).
Step 4: The result from the calculation is approximately 36.87 degrees.
Step 5: Round 36.87 degrees to the nearest whole number, which is 37 degrees.

Trigonometric Functions – Understanding the relationship between angles and their cosine values.
Inverse Trigonometric Functions – Using the arccos function to find the angle corresponding to a given cosine value.
Rounding – Rounding the result to the nearest degree as specified in the question.