Are these trig identities correct?

In summary, the conversation discusses the trigonometric identities for cos(90+theta) and sin(90+theta) and clarifies that cos is negative in the second quadrant while sin is positive. The conversation also mentions using the unit circle and sums/differences or cofunction identities to verify the solutions being discussed.
  • #1
rocomath
1,755
1
cos(90+theta) = sin(theta)

sin(90+theta) = -cos(theta)

cos is negative in 2nd quad

sin is positive in 2nd quad

i'm looking at some soln's and i just need clarification, thanks!
 
Last edited:
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  • #2
rocophysics said:
cos(90+theta) = sin(theta)

sin(90+theta) = -cos(theta)

thanks!
Refer to the unit circle and you can answer this yourself.
 
  • #3
No, they are not. Do you know an expression for cos(x+90) and sin(x+90), or more generally cos(a+b) and sin(a+b)?
 
  • #4
cristo said:
No, they are not. Do you know an expression for cos(x+90) and sin(x+90), or more generally cos(a+b) and sin(a+b)?
lol ah! why didn't it click, thanks again cristo :-]

let me verify these soln's I'm typing up by using the sums/differences or cofunction identities.
 

1. What are trigonometric identities?

Trigonometric identities are mathematical equations that involve trigonometric functions such as sine, cosine, and tangent. They are used to simplify and solve trigonometric equations and expressions.

2. How do I know if a trig identity is correct?

To verify the correctness of a trigonometric identity, you can use algebraic manipulation to show that both sides of the equation are equal. You can also use a calculator to plug in values for the variables and see if both sides of the equation give the same result.

3. Can I use trig identities to solve equations?

Yes, trig identities can be used to simplify and solve trigonometric equations. They can also be used to prove other trigonometric identities.

4. Are there specific steps to follow when using trig identities?

Yes, there are several steps you can follow when using trig identities. First, identify the type of identity you are dealing with (e.g. Pythagorean, sum and difference, double angle). Then, use algebraic manipulation and substitution to simplify the equation. Finally, check your solution by plugging in values for the variables or using a calculator.

5. Can I create my own trig identities?

Yes, you can create your own trigonometric identities by using algebraic manipulations and substitutions on existing identities. However, it is important to verify the correctness of your new identity before using it in any calculations.

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