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Answer:
sin t =
cos t =
tan t =
csc t =
sec t =
cot t =
Step-by-step explanation:
In the unit circle:
- x-coordinate of a point on the circle represents cosine the angle between the + ve part of x-axis and the terminal side which joins the center of the circle and this point
- y-coordinate of a point on the circle represents sine the angle between + ve part of x-axis and the terminal side which joins the center of the circle and this point
In the attached figure
∵ t represents the angle between + ve part of x-axis
and the terminal side drawn from the center of the circle to
point P
∴ The coordinates of point P are (cos t , sin t)
∵ The coordinates of P are ( ,
)
∴ sin t =
∴ cos t =
∵ tan t =
- Substitute the values of sin t and cos t
∴ tan t =
- Multiply up and down by 5 to simplify the fraction
∴ tan t =
∵ csc t =
- Reciprocal the value of sin t
∴ csc t =
∵ sec t =
- Reciprocal the value of cos t
∴ sec t =
∵ cot t =
- Reciprocal the value of tan t
∴ cot t =