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6. More about Trigonometry (a) How to memorize the trigonometric identities? Trigonometric Identities Easy Memory Tips: Convert the trigonometric ratios with the angles 180o± and 360o± . 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 III IV I is acute 180 - o 180 + 360o- 360o+ sinsin sin sin - sin - sin sin coscos cos - cos - cos cos cos tantan tan - tan tan - tan tan o 6. More about Trigonometry (a) How to memorize the trigonometric identities? Trigonometric Identities Easy Memory Tips: Convert the trigonometric ratios with the angles 90o± and 270o± . 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 III IV is obtuse 90o- 90o+ 270o- 270o+ sincos sin cos cos - cos - cos cos sin 1 tan - sin 1 - tan - sin 1 tan sin 1 - tan cossin tan 1 tan tan 6. More about Trigonometry (b) For 0 ≤ ≤360 , how to solve the trigonometric equations? o E.g. o Solve the equation sin = -0.5. Consider sin = 0.5 first. + = 30o (Use calculator to calculate the answer) ∵ sin < 0 ∴ lies in quadrants III or IV + Sin All S A T C 180o+ ∵ The symbol of sine does not change - ∴ We only need to consider 180o+ and 360o- i.e. = 180o+30o or = 360o- 30o = 210o or = 330o 360o- -