Answer:
sin t = [tex]\frac{3}{5}[/tex]
cos t = [tex]-\frac{4}{5}[/tex]
tan t = [tex]-\frac{3}{4}[/tex]
csc t = [tex]\frac{5}{3}[/tex]
sec t = [tex]-\frac{5}{4}[/tex]
cot t = [tex]-\frac{4}{3}[/tex]
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 ( [tex]-\frac{4}{5}[/tex] , [tex]\frac{3}{5}[/tex] )
∴ sin t = [tex]\frac{3}{5}[/tex]
∴ cos t = [tex]-\frac{4}{5}[/tex]
∵ tan t = [tex]\frac{sin(t)}{cos(t)}[/tex]
- Substitute the values of sin t and cos t
∴ tan t = [tex]\frac{\frac{3}{5}}{-\frac{4}{5}}[/tex]
- Multiply up and down by 5 to simplify the fraction
∴ tan t = [tex]-\frac{3}{4}[/tex]
∵ csc t = [tex]\frac{1}{sin(t)}[/tex]
- Reciprocal the value of sin t
∴ csc t = [tex]\frac{5}{3}[/tex]
∵ sec t = [tex]\frac{1}{cos(t)}[/tex]
- Reciprocal the value of cos t
∴ sec t = [tex]-\frac{5}{4}[/tex]
∵ cot t = [tex]\frac{1}{tan(t)}[/tex]
- Reciprocal the value of tan t
∴ cot t = [tex]-\frac{4}{3}[/tex]
