Stephen Su Quan Yuan's answer to Daddy's Secondary 3 A Maths Singapore question.

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Stephen Su Quan Yuan
Stephen Su Quan Yuan's answer
87 answers (Tutor Details)
1st
Your current workings need to be refined. There are a lot of steps missing and you got to input the workings to get marks.

Suppose an equation of the form sin⁡x=k,cos⁡x=k or tan⁡x=k, where k is a constant, is given. The equation can be solved for 0°≤x≤360° (or 0≤x≤2π) by performing these steps:

Step 1: Use the ASTC rule to decide the quadrants in which x lies by considering the sign of k. Best step to do here: Draw the quadrants and label all angles x.

Step 2: Find the reference angle α. Check that α is measured in degrees or radians. Note that the trigo ratio of the reference angle WILL BE POSITIVE, so always trigo inverse the positive trigo ratio to find reference angle α.
Draw the 2 special-angled triangles if necessary.

Step 3: Use α to find x in the required quadrants.
When x is in degrees: x=α,x=180°-α,180°+α, or 360°-α (1st, 2nd, 3rd, 4th respectively)

When x is in radians: x=α,π-α,π+α, or 2π-α (1st, 2nd, 3rd, 4th respectively)