Cos(t)=24/25, what does sin(t)=?

1 answer:

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Answer:

The value of sin t is $\frac{7}{25}$

Step-by-step explanation:

Given as :

cos (t) = $\frac{24}{25}$

Since sin² t + cos² t = 1

So, sin² t = 1 - cos² t

or, sin² t = 1 - ( $\frac{24}{25}$ )²

or, sin² t = $\frac{25^{2} - 24^{2} }{25^{2} }$

Or, sin² t = $\frac{625 - 576}{625}$

Or , sin² t = $\frac{49}{625}$

Or, sin t = $\sqrt{\frac{49}{625} }$

So, sin t = $\frac{7}{25}$

Hence The value of sin t is $\frac{7}{25}$ Answer

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Explanation:

Conversion of a quadratic equation from standard form to vertex form is done by completing the square method.

Assume the quadratic equation to be $\mathbf{ax^{2}+bx+c=0}$ where x is the variable.

Completing the square method is as follows:

send the constant term to other side of equal $\mathbf{ax^{2}+bx=-c}$
divide the whole equation be coefficient of $\mathbf{x^{2}}$ , this will give $\mathbf{x^{2}+\frac{b}{a}x=- \frac{c}{a}}$
add $\mathbf{(\frac{b}{2a})^{2}}$ to both side of equality $\mathbf{x^{2}+2\times\frac{b}{2a}x+\frac{b}{2a}^{2}=-\frac{c}{a}+\frac{b}{2a}^{2}}$
Make one fraction on the right side and compress the expression on the left side $\mathbf{(x+\frac{b}{2a})^{2}=\frac{b^{2}-4ac}{4a^{2}}}$
rearrange the terms will give the vertex form of standard quadratic equation $\mathbf{a(x+\frac{b}{2a})^{2}-\frac{b^{2}-4ac}{4a}=0}$