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Introduction to trigonometry (sine, cosine, tangent)
Take note that short forms can be used to remember sine, cosine and tangent.
TOA → TanӨ = Opposite side ÷ Adjacent side
CAH → CosӨ = Adjacent side ÷ Hypotenuse
SOH → SinӨ = Opposite side ÷ Hypotenuse
TOA → TanӨ = Opposite side ÷ Adjacent side
CAH → CosӨ = Adjacent side ÷ Hypotenuse
SOH → SinӨ = Opposite side ÷ Hypotenuse
Introduction to quadrant rule (CAST)
1st quadrant (0˚ to 90˚) → ALL trigonometric ratios are +ve
2nd quadrant (90˚ to 180˚) → Only Sine of the angle is +ve
3rd quadrant (180˚ to 270˚) → Only Tangent of the angle is +ve
4th quadrant (270˚ to 360˚) → Only Cosine of the angle is +ve
This quadrant rule can be remembered as CAST. Quadrant rule is a very useful and essential method used in solving trigonometric equations to find angles within a given range. Do learn and remember it well.
For students taking E Maths only, using the quadrant rule, the following two identities can be derived.
sin A = sin (180˚ - A)
cos A = -cos (180˚ - A)
These two identities are important to remember.
2nd quadrant (90˚ to 180˚) → Only Sine of the angle is +ve
3rd quadrant (180˚ to 270˚) → Only Tangent of the angle is +ve
4th quadrant (270˚ to 360˚) → Only Cosine of the angle is +ve
This quadrant rule can be remembered as CAST. Quadrant rule is a very useful and essential method used in solving trigonometric equations to find angles within a given range. Do learn and remember it well.
For students taking E Maths only, using the quadrant rule, the following two identities can be derived.
sin A = sin (180˚ - A)
cos A = -cos (180˚ - A)
These two identities are important to remember.
Solving simple trigonometric equations by quadrant rule (sinӨ=+ve value) (*Note that the identity sin A = sin (180˚ - A) can thus be derived since sine of angle A in first quadrant and sine of angle (180˚ - A) in second quadrant both give +ve equal values)
Solving simple trigonometric equations by quadrant rule (sinӨ=-ve value)
Solving simple trigonometric equations by quadrant rule (cosӨ=+ve value)
Solving simple trigonometric equations by quadrant rule (cosӨ=-ve value) (*Note that the identity cos A = -cos (180˚ - A) can thus be derived since cosine of angle A in first quadrant and cosine of angle (180˚ - A) in second quadrant both give same numerical values except in first quadrant the value is +ve while in second quadrant the value is -ve)
Solving trigonometric problems involving angles of elevation and depression (simple problem)
Take note that shown in this video, angle of elevation and angle of depression both have the same values as the two angles are alternate angles (alt. angles).
Being able to understand angle of elevation and angle of depression well is important as more difficult questions on the topic bearings will usually ask on angle of elevation and depression together with the application of sine rule and cosine rule (refer to further trigonometry) being asked.
Being able to understand angle of elevation and angle of depression well is important as more difficult questions on the topic bearings will usually ask on angle of elevation and depression together with the application of sine rule and cosine rule (refer to further trigonometry) being asked.