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cos(x)=(-1/2 (0.5)(9))/((0.8)(0.5)(9.8))

Solution

cos (x) = \frac{- \frac{1}{2} ( 0.5 ) ( 9 )}{( 0.8 ) ( 0.5 ) ( 9.8 )}

x = 2.18215 \dots + 2 πn, x = - 2.18215 \dots + 2 πn

Radians

x = 2.18215 \dots + 6.28318 \dots n, x = - 2.18215 \dots + 6.28318 \dots n

Solution steps

cos (x) = \frac{- \frac{1}{2} ( 0.5 ) ( 9 )}{( 0.8 ) ( 0.5 ) ( 9.8 )}

Simplify

\frac{- \frac{1}{2} \cdot 0.5 \cdot 9}{0.8 \cdot 0.5 \cdot 9.8} : - \frac{4.5}{7.84}

\frac{- \frac{1}{2} \cdot 0.5 \cdot 9}{0.8 \cdot 0.5 \cdot 9.8}

Multiply the numbers:

0.5 \cdot 9 = 4.5

= \frac{- 4.5 \cdot \frac{1}{2}}{0.8 \cdot 0.5 \cdot 9.8}

Multiply the numbers:

0.8 \cdot 0.5 \cdot 9.8 = 3.92

= \frac{- 4.5 \cdot \frac{1}{2}}{3.92}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{4.5 \cdot \frac{1}{2}}{3.92}

Multiply

4.5 \cdot \frac{1}{2} : \frac{4.5}{2}

4.5 \cdot \frac{1}{2}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot 4.5}{2}

Multiply the numbers:

1 \cdot 4.5 = 4.5

= \frac{4.5}{2}

= - \frac{\frac{4.5}{2}}{3.92}

Simplify

\frac{\frac{4.5}{2}}{3.92} : \frac{4.5}{7.84}

\frac{\frac{4.5}{2}}{3.92}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{4.5}{2 \cdot 3.92}

Multiply the numbers:

2 \cdot 3.92 = 7.84

= \frac{4.5}{7.84}

= - \frac{4.5}{7.84}

cos (x) = - \frac{4.5}{7.84}

Apply trig inverse properties

cos (x) = - \frac{4.5}{7.84}

General solutions for

cos (x) = - \frac{4.5}{7.84}

cos (x) = - a \Rightarrow x = arccos (- a) + 2 πn, x = - arccos (- a) + 2 πn

x = arccos (- \frac{4.5}{7.84}) + 2 πn, x = - arccos (- \frac{4.5}{7.84}) + 2 πn

x = arccos (- \frac{4.5}{7.84}) + 2 πn, x = - arccos (- \frac{4.5}{7.84}) + 2 πn

Show solutions in decimal form

x = 2.18215 \dots + 2 πn, x = - 2.18215 \dots + 2 πn

cos (2 a) = \frac{31}{81}

\frac{tan ( a ) + 1}{tan ( a )} = 2

1 - cos (x) = \frac{2 sin ^{2} ( x )}{2}

2 sec (2 x) + tan (2 x) - 3 = 0

x, 5 = 9.4 cos (x)