# Solve for t h=7sin(pi/21t)+28

h=7sin(π21t)+28
Rewrite the equation as 7sin(π21t)+28=h.
7sin(π21t)+28=h
Combine π21 and t.
7sin(πt21)+28=h
Subtract 28 from both sides of the equation.
7sin(πt21)=h-28
Divide each term by 7 and simplify.
Divide each term in 7sin(πt21)=h-28 by 7.
7sin(πt21)7=h7+-287
Cancel the common factor of 7.
Cancel the common factor.
7sin(πt21)7=h7+-287
Divide sin(πt21) by 1.
sin(πt21)=h7+-287
sin(πt21)=h7+-287
Divide -28 by 7.
sin(πt21)=h7-4
sin(πt21)=h7-4
Take the inverse sine of both sides of the equation to extract t from inside the sine.
πt21=arcsin(h7-4)
Multiply both sides of the equation by 21π.
21π⋅πt21=21π⋅arcsin(h7-4)
Simplify both sides of the equation.
Cancel the common factor of 21.
Cancel the common factor.
21π⋅πt21=21π⋅arcsin(h7-4)
Rewrite the expression.
1π⋅(πt)=21π⋅arcsin(h7-4)
1π⋅(πt)=21π⋅arcsin(h7-4)
Cancel the common factor of π.
Factor π out of πt.
1π⋅(π(t))=21π⋅arcsin(h7-4)
Cancel the common factor.
1π⋅(πt)=21π⋅arcsin(h7-4)
Rewrite the expression.
t=21π⋅arcsin(h7-4)
t=21π⋅arcsin(h7-4)
Simplify 21π⋅arcsin(h7-4).
Combine 21π and arcsin(h7-4).
t=21arcsin(h7-4)π
Simplify the numerator.
To write –41 as a fraction with a common denominator, multiply by 77.
t=21arcsin(h7+-41⋅77)π
Write each expression with a common denominator of 7, by multiplying each by an appropriate factor of 1.
Combine.
t=21arcsin(h7+-4⋅71⋅7)π
Multiply 7 by 1.
t=21arcsin(h7+-4⋅77)π
t=21arcsin(h7+-4⋅77)π
Combine the numerators over the common denominator.
t=21arcsin(h-4⋅77)π
Multiply -4 by 7.
t=21arcsin(h-287)π
t=21arcsin(h-287)π
t=21arcsin(h-287)π
t=21arcsin(h-287)π
Multiply both sides of the equation by 21π.
21π⋅πt21=21π⋅arcsin(h7-4)
Simplify both sides of the equation.
Cancel the common factor of 21.
Cancel the common factor.
21π⋅πt21=21π⋅arcsin(h7-4)
Rewrite the expression.
1π⋅(πt)=21π⋅arcsin(h7-4)
1π⋅(πt)=21π⋅arcsin(h7-4)
Cancel the common factor of π.
Factor π out of πt.
1π⋅(π(t))=21π⋅arcsin(h7-4)
Cancel the common factor.
1π⋅(πt)=21π⋅arcsin(h7-4)
Rewrite the expression.
t=21π⋅arcsin(h7-4)
t=21π⋅arcsin(h7-4)
Simplify 21π⋅arcsin(h7-4).
Combine 21π and arcsin(h7-4).
t=21arcsin(h7-4)π
Simplify the numerator.
To write –41 as a fraction with a common denominator, multiply by 77.
t=21arcsin(h7+-41⋅77)π
Write each expression with a common denominator of 7, by multiplying each by an appropriate factor of 1.
Combine.
t=21arcsin(h7+-4⋅71⋅7)π
Multiply 7 by 1.
t=21arcsin(h7+-4⋅77)π
t=21arcsin(h7+-4⋅77)π
Combine the numerators over the common denominator.
t=21arcsin(h-4⋅77)π
Multiply -4 by 7.
t=21arcsin(h-287)π
t=21arcsin(h-287)π
t=21arcsin(h-287)π
t=21arcsin(h-287)π
Solve for t h=7sin(pi/21t)+28

### Solving MATH problems

We can solve all math problems. Get help on the web or with our math app

Scroll to top