Trigonometry
If sinθ=135 and θ is acute, find:
* cos θ
* tan θ
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Step-by-Step Solution
Step 1: Understand the given information
We are given the value of sinθ for an acute angle θ. We need to find the values of cosθ and tanθ. We can use the fundamental trigonometric identity relating sine and cosine.
Step 2: Use the Pythagorean Identity to find cos θ
The fundamental trigonometric identity states that sin2θ+cos2θ=1. By substituting the given value of sinθ into this identity, we can solve for cosθ. Since θ is an acute angle (between 0∘ and 90∘), its cosine value must be positive.
Step 3: Find tan θ using sin θ and cos θ
The tangent of an angle is defined as the ratio of its sine to its cosine. Now that we have both sinθ and cosθ, we can easily calculate tanθ.