Trigonometry Questions

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Graph the following function over a one-period interval. y = 3 sec 1/4 x Choose the correct graph below.

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Find the cosine of the angle between A and B with respect to the standard inner product on M22 A =[3 3] and B = [4 2] [3 -1] [3 2] Carry out all calculations exactly and round to 4 decimal places the final answer only

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Suppose tan(a) = 5/8, where 0 ≤ a ≤ π/ 2. The least solution to tan(3x) = 5/8 in [0, 2π) is x = The greatest solution to tan(3x) = 5/8 in [0, 2π) is x =

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Information about △ABC is given. Determine all remaining information about the triangle. Answers must be accurate to three decimal places. If there are multiple triangles with the given information, determine all of them. If a triangle cannot be solved, explain why not. a) A = 60°2 a = 52 b= 6 b) a = 3, b = 8, c = 50°

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Let ∠D be an acute angle such that cos D=0.64. Use a calculator to approximate the measure of ∠D to the nearest tenth of a degree. m∠D ≈ _____. Let ∠D be an acute angle such that tan D = 0.72. Use a calculator to approximate the measure of ∠D to the nearest tenth of a degree.

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The point P(x, y) on the unit circle that corresponds to a real number t is given. Find the value of the indicated trigonometric function at t. (3/4, √7/4) Find sin t. A) 3/4 B) 3√7/7 C) √7/3 D) √7/4

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Complete the following table of values. Express all answers using exact arithmetic--no decimal numbers. Use "sqrt()" if the answer includes a square root. A 30° 45° 60° sin(A) ______ ______ ______ cos(A) ______ ______ ______ tan(A) ______ ______ ______ cot(A) ______ ______ ______ sec(A) ______ ______ ______ csc(A) ______ ______ ______

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Sketch the graph of y = tan( x + π/4) within the interval ( – 2π, 2π) a) What is the period? b) Write the formula for the vertical asymptotes: x = where k is an odd integer, c) List the vertical asymptotes within ( – 2π, 2π): x = d) List all x intercepts as ordered pairs (x, 0) such that – 2π < x < 2π:

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π/3 is the reference angle for 2π/3 and cos (2π/3) = -cos(π/3) For each angle, find its reference angle. Rewrite the trig values using the reference angle. (A) Nearest x-axis angle for 38/7π (B) Reference angle for 38/7π (C) sin (38/7π) = (D) cos (38/7π) = (E) tan (38/7π) = (F) Nearest x-axis angle for 39/7π (G) Reference angle for 39/7π (H) sin (39/7π) = (I) cos (39/7π) = (J) tan (39/7π) =

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Draw g(x) on the graph, using the appropriate button for parent function. g(x)= - 2 sin(4x) + (- 2)

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Complete the following tables (To find the measures of the angles you will need your calculators): Function/Angle : Sine : 3/4,___,___,___,___,___ Cosine: ___,2/3,___,___,___,___ Tangent : ___,___,3/2,___,___,___ Cosecant : ___,___,___,5/4,___,___ Secant : ___,___,___,___,6/7,___ Cotangent : ___,___,___,___,___,7/8 Function/Angle Sine : 1/2,___,___,___,___,___ Cosine: ___,√3/2,___,___,___,___ Tangent : ___,___,1,___,___,___ Cosecant : ___,___,___,7/4,___,___ Secant : ___,___,___,___,9/7,___ Cotangent : ___,___,___,___,___,11/8

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An airplane is heading north at an airspeed of 550 km/hr, but there is a wind blowing from the northwest at 80 km/hr. The plane will end up flying degrees off course The plane's speed relative to the ground will be km/hr