the terminal point ( p(x,y) ) determined by a real number ( t ) is given. find ( sin t ), ( cos t ), and (…

the terminal point ( p(x,y) ) determined by a real number ( t ) is given. find ( sin t ), ( cos t ), and ( \tan t ).\n( left( \frac { 5 } { 13 }, \frac { 12 } { 13 } \right) )\n( sin t = )\n( cos t = )\n( \tan t = )

the terminal point ( p(x,y) ) determined by a real number ( t ) is given. find ( sin t ), ( cos t ), and ( \tan t ).\n( left( \frac { 5 } { 13 }, \frac { 12 } { 13 } \right) )\n( sin t = )\n( cos t = )\n( \tan t = )

Answer

Explanation:

Step1: Recall the definitions

For a terminal point (P(x,y)) on the unit circle (here (x = \frac{5}{13}), (y=\frac{12}{13})), (\sin t=y), (\cos t = x), and (\tan t=\frac{y}{x}).

Step2: Calculate (\sin t)

Since (y = \frac{12}{13}), (\sin t=\frac{12}{13}).

Step3: Calculate (\cos t)

Since (x=\frac{5}{13}), (\cos t=\frac{5}{13}).

Step4: Calculate (\tan t)

(\tan t=\frac{y}{x}=\frac{\frac{12}{13}}{\frac{5}{13}}=\frac{12}{5}).

Answer:

(\sin t=\frac{12}{13}), (\cos t=\frac{5}{13}), (\tan t=\frac{12}{5})