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4.3 Right Triangle Trigonometry Pg. 484 # 6-16 (even), 22-34 (even), 54-60 (even) –Use right triangles to evaluate trigonometric functions –Find function values for 30 degrees, 45 degrees & 60 degrees. Otherwise known as, in radians. –Use equal cofunctions of complements –Use right triangle trig. to solve applied problems
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These relationships holds true for ALL right triangles
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1.Given this right triangle Find the value of all six trig. functions of Θ. Make sure each value is in simplified form.
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All 45 o - 45 o - 90 o triangles on a unit All 30 o - 60 o - 90 o triangles on a unit circle have these side lengths: Special Triangles
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Using the figures only, find the following values: 2.tan 30 o 3.cos 60 o 4.sin 45 o 5.sec 60 o 6.cot 45 o 7.sin 8.csc
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Cofunction Identities, radiansradians Cofunction Identities, degrees degrees sin (90° – x) = cos x cos (90° – x) = sin x tan (90° – x) = cot x cot (90° – x) = tan x sec (90° – x) = csc x csc (90° – x) = sec x Cofunction Identities Trig identitiesTrig identities showing the relationship between sine and cosine, tangent and cotangent, and secant and cosecant. The value of a trig function of an angle equals the value of the cofunction of the complement of the angle.sinecosinetangent cotangentsecantcosecanttrig functionanglecomplement Find a cofunction with the same value as the given expression. 9. sin 46 o 10. cot OR
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11. The distance across a lake (a) is unknown. To find the distance, a surveyor took the measurements shown in the figure. What is the distance across the lake? 12. A flagpole that is 14 meters tall casts a shadow 10 meters long. Find the angle of elevation of the sun to the nearest degree.
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Angles of Elevation: Angles of Depression: Rotate from a horizontal UP Rotate from a horizontal DOWN
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