Problem 1: Find sin(x) and cos(x) in the right triangle shown below. h 8 6
This problem refers to a right triangle ABC with C -90° as seen in the image below. Use a calculator to find sin A, cos A, sin B, cos B. Round your answer to the nearest hundredth. B a A C b a = 1, c-2 sin A - cos A = sin B cos B
Problem 3 (12 points) The curve with parametric equations (1 + 2 sin(9) cos(9), y-(1 + 2 sin(θ)) sin(0) is called a limacon and is shown in the figure below. -1 1. Find the point (x,y 2. Find the slope of the line that is tangent to the graph at θ-π/2. 3. Find the slope of the line that is tangent to the graph at (,y)-(1,0) ) that corresponds to θ-π/2. Problem 3 (12 points) The curve with parametric equations...
In the figure is a right triangle with a hypotenuse of 5. Find the values of the sine, cosine, and tangent of 8. sin (0)- cos (0)- tan()- 5 h.
(1 point) Consider the right triangle illustrated below. Find the sine, cosine and tangent of angles A and B Express all answers using exact values (no decimal numbers) sin cos(0) tan(0) Note: You can eam partial credit on this problem.
iangle is a right triangle.) For the triangle shown in the figure below what are each of the following? (Let y 32.0 m and r -40.0 m. Assume the t (a) the length of the unknown side x 24 b) the tangent of Apply the expressions for tangent of a base angle in a right triangle as a ratio of the sides of the triangle (c) the sin of ssions for the sine of a base angle in a right...
Problem 7. (6 points) Let f(x) = 5 sin(x) 3 + cos(x) Find the following: 1. f'(x)= 2. f'(5) = Note: You can earn partial credit on this problem.
6. (23 pts.) Given: cos(°/2) = -1/4 and "/2</2<311/4. Form a right triangle with the given information. Determine the following and report all numerical answers in exact form. Report angles to two decimal places. a. (02 pts.) The missing side b. (03 pts.) sin(°/2 c. (03 pts.) tancº/2) d. (02 pts.) sin() e. (02 pts.) cos() f. (02 pts.) tan() g. (02 pts.) sin(20) h. (02 pts.) cos(2p) i. (02 pts.) tan(2) 1. (01 pts.) The angle/2 k. (01 pt.)...
Question 1 1 pts Find the derivative of f(x) = cos(sin(3x)). Of"(x) --cos(3x) sin(sin(3x)) O f'() -- 3cos(3x) sin(sin(3x)) Of'(x) - 3cos(3x) sin(cos(3x]) f'x) --sin(3x) cos(cos(3x)) Question 2 1 pts Find the derivative of f(x) = cos(x^2 + 2x). Of "(x)=2x+2 sin(x^2 + 2x) O f'(x)= x^2 sin(x^2+2x) Of"(x)= (2x+ 2) sin(x^2 + 2x) f'(x)= -(x^2 + 2) sin(x^2 + 2x) O f'(x)--(2x + 2) sin(x^2 + 2x) Question 3 1 pts Use implicit differentiation to find the slope of...
5. Prove the following identity. (sin x + cos x) = 1+sin 2x 6. If cos(x) = , and x E QIV , find the exact value of each of the following. a.sin (2x) b.cos cos()
3 12 Smaller Triangle Larger Triangle sin = sin = cos = cos = tan 0= tan (= CSC = CSC = sec = sec = cot 8 = cot = Explain why the function values are the same. The triangles are similar so corresponding sides are proportional. The triangles are congruent so the trigonometric function values must be the same.