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Page 1 of 2 14.7 Using Double- and Half-Angle Formulas 877 Solving a Trigonometric Equation Solve tan 2x + tan x = 0 for 0 ≤ x < 2π. SOLUTION tan 2x + tan x = 0 Write original equation. + tan 1 2 º ta ta n n x 2 x x = 0 Use a double-angle formula. 2 tan x + tan x (1º tan2x)= 0 Multiply each side by 1 ºtan2 x. 2 tan x + tan x º tan3x = 0 Distributive property. 3 tan x º tan3x = 0 ...Air force pt test standards male over 30
Half-Angle Identities These are the same as the identities above, but with the square root of both sides taken, and θ substituted for 2 u .

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Double Angle Formulas sin(2u) = 2sinucosu cos(2u) = cos2 u sin2 u = 2cos2 u 1 = 1 22sin u tan(2u) = 2tanu 1 tan2 u Power-Reducing/Half Angle For-mulas sin2 u= 1 cos(2u) 2 cos2 u= 1+cos(2u) 2 tan2 u= 1 cos(2u) 1+cos(2u) Sum-to-Product Formulas sinu+sinv= 2sin u+v 2 cos u v 2 sinu sinv= 2cos u+v 2 sin u v 2 cosu+cosv= 2cos u+v 2 cos u v 2 cosu ...

MGSE9-12.F.TF.9 Prove addition, subtraction, double and half-angle formulas for sine, cosine, and tangent and use them to solve problems. MGSE9-12.F.TF.4 Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.

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The half‐angle identities for the sine and cosine are derived from two of the cosine identities described earlier. The sign of the two preceding functions depends on the quadrant in which the resulting angle is located. Example 1: Find the exact value for sin 105° using the half‐angle identity.

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Double- and Half-Angle Identities Date_____ Period____ Use a double-angle identity to find the exact value of each expression. 1) sin 120 ° 2) tan 60 ° 3) cos 4 π 3 4) sin 5π 3 Use a half-angle identity to find the exact value of each expression. 5) tan 45 ° 6) sin 165 ° 7) sin 5π 6 8) cos 30 °

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7 6 2 sin 2 cos 2 Lesson 7-4 Double-Angle and Half-Angle Identities 451 Unlike with the double-angles identities, you must determine the sign. If represents the measure of an angle, then the following identities hold for all values of . sin 2 1 2 c os cos 2 1 2 c os tan 2 1 1 c c o o s s, cos 1 Half-Angle Identities Example 2 1 c 2 os 1 c 2 os ...

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4. Develop, prove, and apply the double-angle and half-angle formulas for sine and cosine. (Addison-Wesley §5.4, Glencoe §7.4, §7.5)

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2.5 ~ Double Angle Formulas and Half-Angle Formulas • Develop and use the double and half-angle formulas. • Evaluate trigonometric functions using these formulas. • Verify identities and solve more trigonometric equations.

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Question 444897: How to find the exact value of the angle 67.5 using half-angle identities? It says for sin, cos, and tan... Thanks! Answer by lwsshak3(11628) (Show Source):

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Using Trigonometry to Find Angle Measures Date_____ Period____ Find each angle measure to the nearest degree. 1) tan A = 2.0503 64° 2) cos Z = 0.1219 83° 3) tan Y = 0.6494 33° 4) sin U = 0.8746 61° 5) cos V = 0.6820 47° 6) sin C = 0.2756 16° Find the measure of the indicated angle to the nearest degree. 7) 55 51? 68° 8) 19 27? 45° 9) 34 55

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