Need some help on Grade 11 math

[needshelp]

Hey I was wondering if anyone could help me on a few questions. They are:

1. Evaluate y=cos(theta) for 0degrees is < or equal to theta and < than or equal to 540degrees, when y= -0.7 Answer to the nearest degree.

2.a) Evaluate h(t)= cos (20t)degrees for t=3 ( I know this answer is 0.5 and how to get that but for part B..)

B) What is the value of t when h(t)=0.3 for 0 is <or equal to t and < or equal to 18?

3. Determine all value of theta for which sin theta=cos theta, for -360degrees < or equal to theta < or equal to 360degrees

Thanks for your time.

 

[stapel]

Wow; your book writes really lousy instructions. :shock:

"Evaluate" means "plug in the number for the variable and simplify to get the answer", but they've asked you in the first exercise to solve an equation, not evaluate an expression. No wonder you're confused.

1) This is actually asking you to solve the following:

. . . . .\(\displaystyle \large{\cos{(\theta)}\mbox{ }=\mbox{ }-0.7}\)

Since this isn't one of the basic reference-angle values (like for 30° or 45° or something), then you must have to use the inverse-trig buttons on your calculator, and then use the fact that cosine repeats to find the other angle values that will give the same value for cosine.

(This is where the restricted domain of the inverse function comes in: the calculator button is only going to give you one of the solutions, because that function only "sees" that solution. You have to use your knowledge of cosines to find the rest.)

2-a) For this one, just plug "3" in for "t", and simplify. You can use the basic reference-angle stuff you memorized for this.

2-b) In other words, solve the following:

. . . . .\(\displaystyle \large{\sin{(\theta)}\mbox{ }=\mbox{ }\cos{(\theta)}}\)

You know they aren't equal when cos(@) = 0 (from the graphs) so, even if you've forgotten the basic reference-angle value that gives the solution, you know that the solution will not involve cosine being zero. This fact allows you to divide through by cos(@) to get:

. . . . .\(\displaystyle \large{\frac{\sin{(\theta)}}{\cos{(\theta)}}\mbox{ }=\mbox{ }1}\)

. . . . .\(\displaystyle \large{\tan{(\theta)}\mbox{ }=\mbox{ }1}\)

And you can easily solve this. Then use your knowledge of tangent to find the other solutions within the given interval.

Eliz.