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15.4 Sine and Tangent of a Sum or Difference Sine of a Sum or Difference Identity sin sin cos cos sin Tangent of a Sum or Difference Identity tan tan tan 1 tan tan Express each of the following as a single sine or tangent and evaluate. 1. sin 335 cos110 cos 335 sin110 o o o o Express each of the following as a single sine or tangent and evaluate. tan155 tan 20 o o 1 tan155 tan 20 o 2. o • To use the sum or difference identity to find the value of a trig function, first make sure the angle is in degrees – it is much easier to work with. • Then, you want to find two “nice” numbers that add/subtract to the angle measure. There is more than one answer! • Hint: If your angle ends in a 5, then 45 will be one of the angles. • Then, use the sum or difference identity to find the value of sine or tangent. Use the formulas for the sine and tangent of a sum and difference, then evaluate. 3. sin105 o Use the formulas for the sine and tangent of a sum and difference, then evaluate. 4. tan 15 o Use the formulas for the sine and tangent of a sum and difference, then evaluate. 5. 11 sin 12 Use the formulas for the sine and tangent of a sum and difference, then evaluate. 6. 17 tan 12 7. Find the exact value of each trigonometric function given: 15 cos x ; x 17 2 a. sin x y b. sin x y 4 3 sin y ; y 2 5 2 8. Find the exact value of each trigonometric function given: 24 sin x ; 0 x 25 2 a. sin x y b. sin x y 4 cos y ; 0 y 5 2