Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Double- And Half-Angle Formulas Double-Angle Formulas cos2u cos u sin u 2 2 cos u 1 2 1 2 sin u sin 2u 2 sin u cosu 2 tan u tan 2u 2 1 tan u 2 2 Double- And Half-Angle Formulas Half-Angle Formulas u 1 cosu sin 2 2 u 1 cosu cos 2 2 u 1 cosu sin u tan 2 sin u 1 cosu Evaluating Trigonometric Expressions Evaluate expressions using double- and half-angle formulas. 1 1. sin 15 sin 30 2 3 1 cos 30 1 2 2 2 2 3 1 2 2 2 3 2 Evaluating Trigonometric Expressions Evaluate expressions using double- and half-angle formulas. 1 2. cos 22.5 cos 45 2 2 1 cos 45 1 2 2 2 2 2 1 2 2 2 2 2 Evaluating Trigonometric Expressions Evaluate expressions using double- and half-angle formulas. 1 3. tan 15 tan 30 2 3 1 1 cos 30 2 1 sin 30 2 2 2 3 2 3 1 2 Evaluating Trigonometric Expressions Evaluate expressions using double- and half-angle formulas. 1 4. sin sin 2 6 12 1 cos 3 1 6 2 2 2 2 3 1 2 3 2 2 2 Evaluating Trigonometric Expressions Evaluate expressions using double- and half-angle formulas. 1 5 5 5. cos cos 8 2 4 5 2 1 cos 1 4 2 2 2 2 2 2 2 1 2 2 2 Evaluating Trigonometric Expressions Evaluate expressions using double- and half-angle formulas. 1 6. tan tan 8 2 4 1 cos 4 sin 4 2 1 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 Evaluating Trigonometric Expressions Find the exact value of the function. u 4 7. cos if cos u , 0 u 2 5 2 4 1 9 1 1 cos u 9 5 10 5 2 2 2 3 10 10 Evaluating Trigonometric Expressions Find the exact value of the function. 4 8. tan 2u if sin u , u 5 2 2 tan u 2 1 tan u 4 4 8 2 3 3 2 4 1 3 9 16 9 5 4 tan u 3 -3 8 9 3 7 3 8 3 7 9 24 7 Evaluating Trigonometric Expressions Verify the identity. 9. 2sin 2 x cos 4 x 1 2 2 sin 2 x cos 22 x 1 2 2 2 sin 2 x 1 2 sin 2 x 1 2 11 Evaluating Trigonometric Expressions Verify the identity. 10. sin x cos x 1 sin 2 x 2 sin x 2 sin x cos x cos x 2 2 sin x cos x 2 sin x cos x 1 2 sin xcos x 2 2 1 sin 2 x Evaluating Trigonometric Expressions Solve the equation for 0 < x < 2. 11. sin x cos 2x sin x 1 2 sin x 2 2 sin x sin x 1 0 2 sin x 1 sin x 1 0 2 2 sin x 1 sin x 1 1 5 3 sin x x , , 2 6 6 2 Evaluating Trigonometric Expressions Solve the equation for 0 < x < 2. 12. cos 2x cos x 2 0 2 cos x 1 cos x 2 0 2 2 cos x cos x 3 0 2 cos x 3 cos x 1 0 2 2 cos x 3 cos x 1 3 x cos x 2 Evaluating Trigonometric Expressions