Trigonometry Answers

. How many grams of (g) can be stored in a 10.0 L container at 1000 kPa and 30C?

Find the scalar x- and y-components of the following displacements in the XY-plane: (a) 300 cm at 127° and (b) 500 cm at 220°

A passenger on a steamboat with a water wheel (see picture) notices an object that has become stuck on one of the paddles of the water wheel. She begins to keep track of its position above the water when it is at a point that is 7 m from the surface. The object then moved upwards to its highest point, 16 m above the surface of the water, then, 6 s later, to its lowest point 4 m below the surface of the water. a) Sketch a graph that represents the height of an object above the water, relative to the distance it has traveled for 2 rotations of the water wheel. Graph on the Separate Paper to. b) Determine an equation of the function, represented by this graph.

Am explorer walks 22km due North and then walks 45degrees south east for 47km.what’s the resultant displacement from the origin?

• An explorer walks 22km due North and then 45 degrees south of east for 47km.what’s the resultant displacement from the origin?

The function 𝑓(𝑥)=2𝑐𝑜𝑠 𝑥−3 is defined for the domain 0≤𝑥≤𝜋/2

a. Find the range of 𝑓(𝑥)

b. Find 𝑓^−1(𝑥).

The function 𝑓(𝑥) is defined as 𝑓(𝑥)=𝑎+𝑏cos𝑥, where 𝑎 and 𝑏 are constants. The range of 𝑓(𝑥) is given by −6≤𝑓(𝑥)≤2.

a. Find the values of 𝑎 and 𝑏

b. Solve the equation 𝑓(𝑥)=0 for 0°≤𝑥≤360°

c. Sketch the graph of 𝑦=𝑓(𝑥) for 0°≤𝑥≤360°

Consider 𝑔(𝑥)=4sin3𝑥

a. Write down the period of 𝑔(𝑥)

b. Write down the number of solutions to the equation 𝑔(𝑥)=3, for 0≤𝑥≤2𝜋

c. Starting with the graph of 𝑦=sin𝑥, state the transformations which can be used to sketch 𝑔(𝑥).

Solve the equation √3sin𝜃−cos𝜃=0 for −180°≤𝑥≤180°

Solve the equation 8sin^2𝑥−7=2cos𝑥 for 0≤𝑥≤360°, giving your answers to 1 decimal place.