Why does sin80°csc80° equal 1?

In summary, the equations Sin80°csc80° = 1 and Cos400° • sec40°= 1 simplify to 1 due to the properties of csc and sec functions. The standard angle for 400° is 40° and the value of sec(40) is equal to 1/cos(40).
  • #1
CrossFit415
160
0
I'm on mobile so I can't use regular symbols.

Sin80°csc80° = 1 why does this equal one? Is there multiplication involved here?

I know csc = 1/sin
 
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  • #2
And I also have trouble doing this...

Cos400° • sec40°= 1 I don't understand how they got one.
 
  • #3
CrossFit415 said:
I'm on mobile so I can't use regular symbols.

Sin80°csc80° = 1 why does this equal one? Is there multiplication involved here?

I know csc = 1/sin
More precisely, csc(x) = 1/sin(x), so what can you replace csc(80°) by?
 
  • #4
CrossFit415 said:
And I also have trouble doing this...

Cos400° • sec40°= 1 I don't understand how they got one.
As far as the cosine is concerned, 400° is the same as what standard angle?
 
  • #5
Replace csc80° with 1/sin? U
 
  • #6
CrossFit415 said:
Replace csc80° with 1/sin? U
No - replace csc80° with 1/sin80°.
 
  • #7
CrossFit415 said:
I'm on mobile so I can't use regular symbols.

Sin80°csc80° = 1 why does this equal one? Is there multiplication involved here?

I know csc = 1/sin

Yes, so what is [tex]sin(80^o)\cdot\frac{1}{sin(80^o)}[/tex] ?
 
  • #8
Thanks a lot for the help!
 
  • #9
Mark44 said:
As far as the cosine is concerned, 400° is the same as what standard angle?

Same angle as 40°
 
  • #10
Yes, so cos(400)= cos(40). Now, what is sec(40) equal to?
 
  • #11
HallsofIvy said:
Yes, so cos(400)= cos(40). Now, what is sec(40) equal to?

Cos is the same angle as 40° . sec = 1/cos40° and they cancel out to be 1.
 

Related to Why does sin80°csc80° equal 1?

1. What are the basic trigonometric functions?

The basic trigonometric functions are sine, cosine, and tangent. These functions represent the ratio of the sides of a right triangle and can be used to solve for missing angles or sides.

2. What are trigonometric identities?

Trigonometric identities are equations that are true for all values of the variables involved. They are useful in simplifying trigonometric expressions and solving trigonometric equations.

3. How do you find the value of a trigonometric function?

The value of a trigonometric function can be found using a calculator or by using the unit circle. The unit circle is a circle with a radius of 1 and can be used to find the values of the trigonometric functions for different angles.

4. What is the relationship between trigonometric functions and right triangles?

Trigonometric functions are defined based on the ratios of the sides of a right triangle. The sine function is the ratio of the opposite side to the hypotenuse, cosine is the ratio of the adjacent side to the hypotenuse, and tangent is the ratio of the opposite side to the adjacent side.

5. What are the Pythagorean identities?

The Pythagorean identities are three trigonometric identities that involve the square of trigonometric functions. They are sin²θ + cos²θ = 1, tan²θ + 1 = sec²θ, and cot²θ + 1 = csc²θ. These identities are derived from the Pythagorean theorem.

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