Answer:
sin t = [tex]-\frac{8}{17}[/tex]
cos t = [tex]-\frac{15}{17}[/tex]
tan t = [tex]\frac{8}{15}[/tex]
csc t = [tex]-\frac{17}{8}[/tex]
sec t = [tex]-\frac{17}{15}[/tex]
cot t = [tex]\frac{15}{8}[/tex]
Step-by-step explanation:
In the unit circle:
x-coordinate of any point on the circle represents cosine the angle between the positive part of x-axis and the segment joining the center of the circle and this point
y-coordinate of any point on the circle represents sine the angle between the positive part of x-axis and the segment joining the center of the circle and this point
In the given figure
∵ t represents the angle between the positive part of x-axis
and the segment drawn from the center of the circle and
point P
∴ The coordinates of point P are (cos t , sin t)
∵ The coordinates of P are ( [tex]-\frac{15}{17}[/tex] , [tex]-\frac{8}{17}[/tex] )
∴ sin t = [tex]-\frac{8}{17}[/tex]
∴ cos t = [tex]-\frac{15}{17}[/tex]
∵ tan t = [tex]\frac{sin(t)}{cos(t)}[/tex]
- Substitute the values of sin t and cos t
∴ tan t = [tex]\frac{-\frac{8}{17}}{-\frac{15}{17}}[/tex]
- Multiply up and down by 17 to simplify the fraction
∴ tan t = [tex]\frac{8}{15}[/tex]
∵ csc t = [tex]\frac{1}{sin(t)}[/tex]
- Reciprocal the value of sin t
∴ csc t = [tex]-\frac{17}{8}[/tex]
∵ sec t = [tex]\frac{1}{cos(t)}[/tex]
- Reciprocal the value of cos t
∴ sec t = [tex]-\frac{17}{15}[/tex]
∵ cot t = [tex]\frac{1}{tan(t)}[/tex]
- Reciprocal the value of tan t
∴ cot t = [tex]\frac{15}{8}[/tex]
