State a trigonometric ratio that is equivalent to each of the following trigonometric ratios
Sin 3pie/10
Cos 6pie/7
Sin 3π/10? More like "Sine and Dine", am I right? Well, fear not, because the trigonometric ratio equivalent to sin 3π/10 is cos 7π/10. So, sin 3π/10 and cos 7π/10 go together like spaghetti and meatballs!
Now, onto cos 6π/7. It's just like finding a parking spot in a busy city – tricky, but not impossible! The trigonometric ratio that's equivalent to cos 6π/7 is sin π/7. So, cos 6π/7 and sin π/7 are a perfect match, like peanut butter and jelly!
To find equivalent trigonometric ratios, we can use the fact that sin(x) = cos(π/2 - x).
1. Sin (3π/10) is equivalent to cos(π/2 - 3π/10).
2. Cos (6π/7) is equivalent to sin(π/2 - 6π/7).
To find an equivalent trigonometric ratio for each of the given trigonometric ratios, we can use the fundamental trigonometric identities.
For the trigonometric ratio sin(3π/10), we can use the identity:
sin(π - θ) = sin(θ).
Therefore, sin(3π/10) is equivalent to:
sin(π - 3π/10) = sin(7π/10)
So, an equivalent trigonometric ratio for sin(3π/10) is sin(7π/10).
Now, for the trigonometric ratio cos(6π/7), we can use the identity:
cos(θ + π) = -cos(θ).
Therefore, cos(6π/7) is equivalent to:
-cos(6π/7 + π) = -cos(13π/7 + 7π/7) = -cos(20π/7)
So, an equivalent trigonometric ratio for cos(6π/7) is -cos(20π/7).
How about adding one rotation to your angle
sin 3π/10
= sin (3π/10 + 2π)
= sin (23π/10)
do the same with the second question.
check each one with your calculator