Some Trig Problems

[hismajesty]

Show work:

Verify each identity


Solve each equation over the interval [0,2pi]. Give exact answers (I guess that means radian form.)


Find the complete solution set for each equation. Give exact answers.


Approximate the solutions of the equation in the interval [0,2pi]. Use a graphing calculator.

[Rule]

By answering these questions, would I be doing your homework for you?

[hismajesty]

By answering these questions, would I be doing your homework for you?

Yes, technically. However, this doesn't go down in the gradebook as homework...I just need it for our quiz (it's like a review) which is on Tuesday. Our quizzes are open notes, and I'll need the examples in order to figure out the quiz.

[Yoni]

One

A few loose hints, that probably work most of the time:

Hint 1. Use basic, well-known and accepted trigonometry identities (such as sin(90-x) = cos(x), and tan(x) = 1/cot(x)).
Hint 2. Use the laws of algebra.
Hint 3. Don't work with sec and csc. Change sec to 1/cos and csc to 1/sin.

Note: I just made these up, some or all of them might be unusable on some questions.

Example:

sec(x) - cos(x) =
[sec is not an acceptable form - hint #3]
= (1/cos(x)) - cos(x) =
[laws of algebra: fractions - hint #2]
= (1 - cos^2(x)) / cos(x) =
[known trigonometric identities: sin^2(x) + cos^2(x) = 1 - hint #1]
= sin^2(x) / cos(x) =
[known trigonometric identities: sin(x) / cos(x) = tan(x) - hint #1]
= sin(x) tan(x)



Two

As for solving equations exactly, try to convert it to algebra.
All squares of sines and cosines can be interchanged using a well known identity, so if you can reach an equation containing only sines (and squares of sines) or only cosines (and squares of cosines), you can algebraically solve it as a quadratic equation, and then trigonometrically solve 1 or 2 equations of the form sin(x) = p or cos(x) = p.



Three

Same as "Two", but find all answers, not just in a specific interval. It depends on you knowing the general solution to the basic equation sin(x) = p or cos(x) = p. You can convert tangents to sin/cos's and reach quadratic equations in the same way mentioned above.



Four

Ok, using a graphical calculator is rather technical. Post if you still need help with this one