Exam 6: An Introduction to Trigonometry Via Right Triangles

Determine whether the equation is correct by evaluating each side. Do not use a calculator. $\tan 30 ^ { \circ } = \frac { \sin 60 ^ { \circ } } { 1 + \sin 30 ^ { \circ } }$

Evaluate the expression using the concept of a reference angle. $\cot \left( - 600 ^ { \circ } \right)$

Determine whether the equation is correct by evaluating each side. Do not use a calculator. Note: Notation such as $\sin ^ { 2 } \theta$ stands for $( \sin \theta ) ^ { 2 }$ . $1 - \tan ^ { 2 } 60 ^ { \circ } = \sec ^ { 2 } 60 ^ { \circ }$

Use the following information to express the remaining five trigonometric values as functions of $u$ . Assume that $u$ is positive. Rationalize any denominators that contain radicals. $\sin \theta = - u ^ { 2 } , 270 ^ { \circ } < \theta < 360 ^ { \circ }$

An observer in a lighthouse is $62 \mathrm { ft }$ above the surface of the water. The observer sees a ship and finds the angle of depression to be $0.1 ^ { \circ }$ . Estimate the distance of the ship from the base of the lighthouse.