Sin[θ+(pi/6)] Multiple values?

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In summary, the sin[θ+(pi/6)] function represents the sine of an angle that is shifted by pi/6 radians from the original angle θ. It can have multiple values and its possible values range from -1 to 1, depending on the value of θ. To find its multiple values, one can use the unit circle or a graphing calculator. Sin[θ+(pi/6)] is related to other trigonometric functions through the fundamental trigonometric identity and its derivative and integral can also be expressed in terms of other trigonometric functions.
  • #1
KaleLetendre
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10
Question:
If cosθ=(3/5) and 0<θ<2pi
determine the value of sin[θ+(pi/6)]

Attempt:
θ=cos^-1(3/5)

θ=0.927295218

sin[θ+(pi/6)]=0.992820323

real answer = 0.992820323, -0.39282

How do i find the second value, all i can find is 0.992820323 but not -0.39282
 
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  • #2
KaleLetendre said:
Attempt:
θ=cos^-1(3/5)

θ=0.927295218
This is not the only possibility.
 
  • #3
thank you i understand now
 

1. What does the sin[θ+(pi/6)] function represent?

The sin[θ+(pi/6)] function represents the sine of an angle that is shifted by pi/6 radians from the original angle θ. In other words, it is the sine of an angle that is rotated counterclockwise by 30 degrees from the original angle.

2. What are the possible values of sin[θ+(pi/6)]?

The possible values of sin[θ+(pi/6)] depend on the value of θ. Generally, they can range from -1 to 1, as the sine function has a maximum value of 1 and a minimum value of -1. However, for specific values of θ, such as θ = 0, the function may have a different range of values.

3. Can sin[θ+(pi/6)] have multiple values?

Yes, sin[θ+(pi/6)] can have multiple values. This is because the function is periodic, meaning it repeats itself after a certain interval. Therefore, for a given value of θ, there can be multiple angles that have the same sine value when shifted by pi/6 radians.

4. How do you find the multiple values of sin[θ+(pi/6)]?

To find the multiple values of sin[θ+(pi/6)], you can use the unit circle or a graphing calculator. By rotating an angle θ counterclockwise by pi/6 radians on the unit circle, you can find the corresponding sine value. Alternatively, you can use a graphing calculator to plot the function and find its multiple values for different values of θ.

5. How is sin[θ+(pi/6)] related to other trigonometric functions?

Sin[θ+(pi/6)] is related to other trigonometric functions through the fundamental trigonometric identity: sin²θ + cos²θ = 1. Using this identity, we can express other trigonometric functions, such as cosine and tangent, in terms of sine and vice versa. Additionally, the derivative and integral of sin[θ+(pi/6)] can be expressed in terms of other trigonometric functions.

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