Solve (7S)^2+(8)^2-75cos6^circ

$$( 7 S ) ^ { 2 } + ( 8 ) ^ { 2 } - 75 \cos 6 ^ { \circ }$$

Evaluate

$$49S^{2}-10.5891421526204975$$

Solution Steps

Evaluate trigonometric functions in the problem

$${(7 S)} ^ {2} + {(8)} ^ {2} - 75 \cdot 0.9945218953682733$$

Expand \left(7S\right)^{2}.

$$7^{2}S^{2}+8^{2}-75\times 0.9945218953682733$$

Calculate 7 to the power of 2 and get 49.

$$49S^{2}+8^{2}-75\times 0.9945218953682733$$

Calculate 8 to the power of 2 and get 64.

$$49S^{2}+64-75\times 0.9945218953682733$$

Multiply 75 and 0.9945218953682733 to get 74.5891421526204975.

$$49S^{2}+64-74.5891421526204975$$

Subtract 74.5891421526204975 from 64 to get -10.5891421526204975.

$$49S^{2}-10.5891421526204975$$

Expand

$$49S^{2}-10.5891421526204975$$

Solution Steps

Evaluate trigonometric functions in the problem

$${(7 S)} ^ {2} + {(8)} ^ {2} - 75 \cdot 0.9945218953682733$$

Expand \left(7S\right)^{2}.

$$7^{2}S^{2}+8^{2}-75\times 0.9945218953682733$$

Calculate 7 to the power of 2 and get 49.

$$49S^{2}+8^{2}-75\times 0.9945218953682733$$

Calculate 8 to the power of 2 and get 64.

$$49S^{2}+64-75\times 0.9945218953682733$$

Multiply 75 and 0.9945218953682733 to get 74.5891421526204975.

$$49S^{2}+64-74.5891421526204975$$

Subtract 74.5891421526204975 from 64 to get -10.5891421526204975.

$$49S^{2}-10.5891421526204975$$