Trigonometry

Learning Target Cl: I can perform operations on complex numbers. Perform the requested operation:

Measuring Triangles Learn by Doing Activity Understanding the connection between Right Triangle Trigonometry and the Unit Circle by measuring and physically manipulating right triangles within a circle of radius 1 decimeter. This activity is optimal if you print the page with the One Decimeter ruler and six triangles on colored card stock paper. However, it will also work if all pages are printed on standard printer paper. 1. Print out one copy of each of the following pages. 2. Carefully and accurately cut out the One Decimeter ruler and the six right triangles. 3. Grab a pen or pencil, a calculator, and a straight edge if you have one (not required, but useful). 4. Now you are ready to follow along with the video guide.

Communication 1) Suppose that cos=-0.38. Explain how we can use this information to determine which quadrant(s) is in. 2) Explain the possible pitfall of using Sine Law to solve for the largest angle in a triangle. 3) Triangle ABC has sides a = 8, b = 6 and angle B = 40°. Sidney notices that this is an ambiguous case and concludes that since ab, the triangle has one solution. Explain clearly why this is incorrect. Include a sketch supporting your answer. 4) True or False: 405° = -315°. Explain clearly, using sketches to support your answer. 5) True or False: If sinA = sinB then we can conclude that Z4=<B. Explain clearly including sketches.

Find x so that function f (x) = lg (√x² – 12x +11) is defined.

Find the functions f(x) = (3+2x²)^2/3 derivative's value when x=1.

Find the derivatives of the functions a) f(x) = sin^4(4x) b) g(x) = cos³ (3x) c) h(x) = tan² (2x)

For what value(s) of k does the equation 5x²-kx+5=0 have no roots?

Trigonometry & Exponential models Find the zeros of the functions h (x) = 42³ (2² — 18) derivative.

The function h(t)=-5r² +20r+1 gives the approximate height, h metres, of a thrown football as a function of time, seconds, since it was thrown. (i) Complete the square. (iii) When did the football reach its maximum height? (iii) What was the maximum height of the football?

Simplify 2m² + 5m / m² +4m-21 + 2m² +13m +20 / m² +m-12 State any restrictions on the variables.