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cos(θ)= 1/4 \land 0>θ>90,tan(θ)

Solution

cos (θ) = \frac{1}{4} and 0^{\circ} > θ > 9 0^{\circ}, tan (θ)

No Solution

Solution steps

cos (θ) = \frac{1}{4} and 0^{\circ} > θ > 9 0^{\circ}

cos (θ) = \frac{1}{4} : θ = 1.31811 \dots + 2 πn, θ = 2 π - 1.31811 \dots + 2 πn

cos (θ) = \frac{1}{4}

Apply trig inverse properties

cos (θ) = \frac{1}{4}

General solutions for

cos (θ) = \frac{1}{4}

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

θ = arccos (\frac{1}{4}) + 2 πn, θ = 2 π - arccos (\frac{1}{4}) + 2 πn

θ = arccos (\frac{1}{4}) + 2 πn, θ = 2 π - arccos (\frac{1}{4}) + 2 πn

Show solutions in decimal form

θ = 1.31811 \dots + 2 πn, θ = 2 π - 1.31811 \dots + 2 πn

0^{\circ} > θ > 9 0^{\circ} :

No Solution

0^{\circ} > θ > 9 0^{\circ}

a > u > b

then

a > u and u > b

0^{\circ} > θ and θ > 9 0^{\circ}

0^{\circ} > θ : θ < 0

0^{\circ} > θ

Switch sides

θ < 0^{\circ}

Apply rule

0^{a} = 0

θ < 0

Combine the intervals

θ < 0 and θ > 9 0^{\circ}

Merge Overlapping Intervals

θ < 0 and θ > 9 0^{\circ}

The intersection of two intervals is the set of numbers which are in both intervals

θ < 0

and

θ > 9 0^{\circ}

No Solution

No Solution

Combine the intervals

(θ = 1.31811 \dots + 2 πn or θ = 2 π - 1.31811 \dots + 2 πn) and No Solution

Merge Overlapping Intervals

No Solution