If sin6y = cos9y , then y is equal to (1) 1.5 (2) 36 (3) 6 (4) 54

Set up equation: We know that the sine and cosine functions are co-functions, meaning that sin(θ) = cos(90° - θ) for angles measured in degrees. Therefore, we can set up the equation sin6y = cos9y as sin6y = cos(90° - 6y).Equate angles: Now we can equate the angles inside the sine and cosine functions: 6y = 90° - 9y.Add and solve: To solve for y, we add 9y to both sides of the equation: 6y + 9y = 90°.Combine terms: Combining like terms, we get 15y = 90°.Divide and solve: Now we divide both sides by 15 to solve for y: y = 90° / 15.Calculate final value: Calculating the division, we find y = 6°.

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If $\sin 6y = \cos 9y$ , then $y$ is equal to $\newline$ ( $1$ ) $1.5$ $\newline$ ( $2$ ) $36$ $\newline$ ( $3$ ) $6$ $\newline$ ( $4$ ) $54$

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Math Problems

Grade 6

Estimate products of fractions and whole numbers

Full solution

Q. If

\sin 6y = \cos 9y

, then

y

is equal to

\newline

(

1

)

1.5

\newline

(

2

)

36

\newline

(

3

)

6

\newline

(

4

)

54

Set up equation: We know that the sine and cosine functions are co-functions, meaning that $\sin(\theta) = \cos(90° - \theta)$ for angles measured in degrees. Therefore, we can set up the equation $\sin(6y) = \cos(9y)$ as $\sin(6y) = \cos(90° - 6y)$ .
Equate angles: Now we can equate the angles inside the sine and cosine functions: $6y = 90° - 9y$ .
Add and solve: To solve for $y$ , we add $9y$ to both sides of the equation: $6y + 9y = 90°$ .
Combine terms: Combining like terms, we get $15y = 90^\circ$ .
Divide and solve: Now we divide both sides by $15$ to solve for $y$ : $y = \frac{90°}{15}$ .
Calculate final value: Calculating the division, we find $y = 6^\circ$ .