6 More about Trigonometry a How to memorize

6. More about Trigonometry (a) How to memorize the trigonometric identities? Trigonometric Identities Easy Memory Tips: Convert the trigonometric ratios with the angles 180 o± and 360 o± . The symbol of sine/cosine/tangent remains unchanged. Write the angle as . According to the quadrant that the angle lies in, determine the sign of the trigonometric ratio. Only sin is +ve Only tan is +ve All ratio are +ve S A T C Only cos is +ve Quadrant II IV I is acute 180 o- 180 o+ 360 o- 360 o+ sin sin - sin cos cos - cos tan tan - tan

6. More about Trigonometry (a) How to memorize the trigonometric identities? Trigonometric Identities Easy Memory Tips: Convert the trigonometric ratios with the angles 90 o± and 270 o± . The symbol of sine/cosine/tangent is changed. Write the angle as . According to the quadrant that the angle lies in, determine the sign of the trigonometric ratio. Only sin is +ve Only tan is +ve All ratio are +ve S A T C Only cos is +ve Quadrant I II IV is obtuse 90 o- 90 o+ 270 o- 270 o+ sin cos - cos sin - sin tan - - tan

6. More about Trigonometry (b) For 0 o≤ ≤ 360 o, how to solve the trigonometric equations? E. g. Solve the equation sin = -0. 5. Consider sin = 0. 5 first. + = 30 o (Use calculator to calculate the answer) ∵ sin < 0 ∴ lies in quadrants III or IV Sin All S A 180 o+ T C 360 o- ∵ The symbol of sine does not change - ∴ We only need to consider 180 o+ and 360 o- i. e. = 180 o+ 30 o or = 360 o- 30 o = 210 o or = 330 o + -