Trigonometry Questions & Answers

When I stand 27 m away from a tree on the second floor of my home, the angle of elevation to the top of the tree is \( 53^{\circ} \) and the angle of depression to the base of the tree is \( 10^{\circ} \). What is the height of the tree?

\( \frac{1+\sin (2\alpha )+\cos (2\alpha )}{1+\sin (2\alpha )-\cos (2\alpha )}=\cot (\alpha ) \)

Si a ciertahora el ánqulo de depresión del sol es de \( 79^{\circ} \), ¿Cuánto midé la sombra de un mastil de 15 m de altura?

The Bungling Brothers Circus is in town and you are part of the crew that is setting up its enormous tent. The center pole that holds up the tent is 70 feet tall. To keep it upright, a support cable needs to be attached to the top of the pole so that the cable forms a \( 60^{\circ} \) angle with the ground. a) How long is the cable? b) How far from the pole should the cable be attached to the ground? Nathan is standing in a meadow, exactly 185 feet from the base of El Capitan. At \( 11: 00 \) a m , he observes Emily climbing up the wall and determines that his angle of sight up to Emily is about \( 10^{\circ} \). If Nathan's eyes are about 6 feet above the ground, about how high is Emily at \( 11: 00 \) a m?

9. Si: \( \cos x+\operatorname{Cos} y+\cos z=0 \) Calcular: \( P=\frac{\operatorname{Cos} 3 x+\cos 3 y+\cos z}{\operatorname{Cos} x \operatorname{Cos} y \operatorname{Cos} z} \)

\( \operatorname { lor } \operatorname { de } A = \sin 105 ^ { \circ } + \cos 105 ^ { \circ } \)

4.3 Without using a calculator, determine the value of: \( \begin{array}{l}4.3 .1 \quad \frac{\sin 30^{\circ} \cdot \cot 45^{\circ}}{\cos 30^{\circ} \cdot \tan 60^{\circ}} \\ 4.3 .2 \quad \sin ^{2} 30^{\circ}-\cos 60^{\circ} \cdot \sqrt{\tan 45^{\circ}}\end{array} \)

places. 4.2 .1 \( \cos 2 A-\sin \left(\frac{1}{2} B\right) \) \( 4.2 .2 \quad 2 \tan ^{2} B \)

places. 4.2 .1 \( \cos 2 A-\sin \left(\frac{1}{2} B\right) \) \( 4.2 .2 \quad 2 \tan ^{2} B \)

QUESTION 6 6.1 Given that \( f(x)=-3 \sin x \) and \( g(x)=\cos x+1 \) where \( x \varepsilon\left[0^{\circ} ; 360^{\circ}\right] \) 6.1 .1 Write down the amplitude of \( f(x) \). 6.1 .2 What is the period of \( g(x) \). 6.1 .3 On the same set of axes, sketch the graphs of \( f(x) \) and \( g(x) \) and clearly show all (1) (5) the intereepts with the axes and the turning points.