Q. Express as a function of a DIFFERENT angle, 0∘≤θ<360∘.cos(5∘)cos(□∘)
Understand co-terminal angles: Understand the concept of co-terminal angles. Co-terminal angles are angles that share the same initial and terminal sides. An angle's co-terminal can be found by adding or subtracting multiples of 360∘ (for degrees) or 2π (for radians).
Find co-terminal angle: Find a co-terminal angle of 5° that is within the range 0° \leq \theta < 360°.Since 5° is already within the given range, we can find a co-terminal angle by adding 360° to 5°.Co-terminal angle = 5°+360°=365°
Express in terms of cos: Express cos(5°) in terms of cos(365°).Since cos(θ)=cos(θ+360°n), where n is an integer, we can express cos(5°) as cos(365°).
Verify range: Verify that the new expression is within the range. 365∘ is not within the range 0^\circ \leq \theta < 360^\circ, so we cannot use it as the final answer. We need to find a different expression that is within the range.
Use angle identities: Use angle identities to express cos(5∘) in terms of a different angle.We can use the identity cos(θ)=cos(−θ) to find a different expression for cos(5∘). This identity allows us to use the negative of the angle, which is within the range.cos(5∘)=cos(−5∘)
Verify new expression: Verify that the new expression is within the range.−5° is within the range 0° \leq \theta < 360° because when we add 360° to −5°, we get 355°, which is within the range.cos(5°)=cos(355°)
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