Precalculus Examples

$x = 80 \cos (38) t$ , $y = 8.7 + 80 \sin (38) t - 16 t^{2}$

Step 1

Simplify $80 \cos (38) t$ .

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Evaluate $\cos (38)$ .

$x = 80 \cdot (0.78801075 t)$

$y = 8.7 + 80 \sin (38) t - 16 t^{2}$

Multiply $80$ by $0.78801075$ .

$x = 63.04086028 t$

$y = 8.7 + 80 \sin (38) t - 16 t^{2}$

$x = 63.04086028 t$

$y = 8.7 + 80 \sin (38) t - 16 t^{2}$

Step 2

Simplify $8.7 + 80 \sin (38) t - 16 t^{2}$ .

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Simplify each term.

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Evaluate $\sin (38)$ .

$y = 8.7 + 80 \cdot (0.61566147 t) - 16 t^{2}$

$x = 63.04086028 t$

Multiply $80$ by $0.61566147$ .

$y = 8.7 + 49.25291802 t - 16 t^{2}$

$x = 63.04086028 t$

$y = 8.7 + 49.25291802 t - 16 t^{2}$

$x = 63.04086028 t$

Simplify the expression.

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Move $8.7$ .

$y = 49.25291802 t - 16 t^{2} + 8.7$

$x = 63.04086028 t$

Reorder $49.25291802 t$ and $- 16 t^{2}$ .

$y = - 16 t^{2} + 49.25291802 t + 8.7$

$x = 63.04086028 t$

$y = - 16 t^{2} + 49.25291802 t + 8.7$

$x = 63.04086028 t$

$y = - 16 t^{2} + 49.25291802 t + 8.7$

$x = 63.04086028 t$

Step 3

Solve the equation for $t$ .

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Simplify $80 \cos (38) t$ .

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Evaluate $\cos (38)$ .

$63.04086028 t = 80 \cdot (0.78801075 t)$

$y = - 16 t^{2} + 49.25291802 t + 8.7$

Multiply $80$ by $0.78801075$ .

$63.04086028 t = 63.04086028 t$

$y = - 16 t^{2} + 49.25291802 t + 8.7$

$63.04086028 t = 63.04086028 t$

$y = - 16 t^{2} + 49.25291802 t + 8.7$

Move all terms containing $t$ to the left side of the equation.

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Subtract $63.04086028 t$ from both sides of the equation.

$63.04086028 t - 63.04086028 t = 0$

$y = - 16 t^{2} + 49.25291802 t + 8.7$

Subtract $63.04086028 t$ from $63.04086028 t$ .

$0 t = 0$

$y = - 16 t^{2} + 49.25291802 t + 8.7$

Multiply $0$ by $t$ .

$0 = 0$

$y = - 16 t^{2} + 49.25291802 t + 8.7$

$0 = 0$

$y = - 16 t^{2} + 49.25291802 t + 8.7$

Since $0 = 0$ , the equation will always be true.

Always true

$y = - 16 t^{2} + 49.25291802 t + 8.7$

Always true

$y = - 16 t^{2} + 49.25291802 t + 8.7$