SPM 2017 Add Maths Paper 1, Question 15Trigonometric Functions

Solved on video in English and Bahasa Melayu · 4 marks · Form 5, Trigonometric Functions · 5:08 video

The question

It is given that cos alpha = t where t is a constant and 0 degrees <= alpha <= 90 degrees. Express in terms of t (a) sin(180 degrees + alpha), (b) sec 2alpha.

[4 marks]

SPM 2017 Add Maths Paper 1, Question 15: the question as drawn in Eduly's video5:08

Step 1

Since 0 <= alpha <= 90 degrees, sin alpha >= 0, so from cos alpha = t, sin alpha = sqrt(1 - t².

Why this step

We only know cos α, but part (a) needs sin α. Since α is acute, sin α is positive, so we take the positive root only.

2 more steps, each with the reason for it, in the full solution

Final answer

(a) −√(1 − t²), (b) 1/(2t² − 1)

Where students lose marks

Watch out: sin(180° + α) is −sin α, not sin α. Use cos 2α = 2cos² α − 1 to stay in t.

Watch every step of this question solved on video (5:08), with the reason behind each step and a box that checks your own answer.

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