Trigonometry Questions & Answers

MATHEMATICS P2 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 \( g(x) \).

(ECNOV 2024) QUESTION 6 \( \begin{array}{llll}6.1 & \text { Given that } f(x)=-3 \sin x \text { and } g(x)=\cos x+1 \text { where } x \varepsilon\left[0^{\circ} ; 360^{\circ}\right] \\ & 6.1 .1 \quad \text { Write down the amplitude of } f(x) .\end{array} \)

5.1 Determine the size of the following angles: 5.1.1 \( \quad \sin \beta+2=2.65 \) \( 5.1 .2 \quad \cos 2 \alpha=0.6 \)

9 Écrire le plus simplement possible: 1) \( \sin (\pi-x)-\cos \left(\frac{\pi}{2}+x\right) \) 2) \( \cos \left(x+\frac{21 \pi}{2}\right)+\cos \left(x-\frac{19 \pi}{2}\right) \)

B Calculer les valeurs exactes des cosinus, sinus et tangente des nombres revels suivants : \( \frac{25 \pi}{3} ;-\frac{97 \pi}{3} ; \frac{5 \pi}{6} ;-\frac{11 \pi}{4} ; \frac{109 \pi}{3} ; \frac{22 \pi}{3} \) 9 Ecrire le plus simplement possible: (1) \( \sin (\pi-x)-\cos \left(\frac{\pi}{2}+x\right) \) (2) \( \cos \left(x+\frac{21 \pi}{2}\right)+\cos \left(x-\frac{19 \pi}{2}\right) \). \( \quad 10 \) Ecrire plus simplement l'expression : \( \sin (\pi-x)+\cos (5 \pi+x)+\sin (4 \pi-x)+\cos (8 \pi+x) \) (1) \( \sin (x+\pi)+\cos (x-\pi)-\sin (x-2 \pi)+\cos (x+5 \pi) \) (2) \( \cos \left(\frac{\pi}{2}-x\right)-\sin \left(x+\frac{\pi}{2}\right)+\cos \left(\frac{7 \pi}{2}-x\right)-\sin \left(x+\frac{5 \pi}{2}\right) \) (3) \( \tan \left(\frac{\pi}{2}-x\right)+\frac{1}{\tan \left(x+\frac{\pi}{2}\right)}-\tan \left(\frac{7 \pi}{2}+x\right)-\frac{1}{\tan \left(\frac{7 \pi}{2}-x\right)} \) (4) \( \cos (\pi+x)+\cos (\pi-x)+\cos (-x) \) (5) \( \sin (\pi+x)+\sin (\pi-x)+\sin (-x) \) (6) \( \sin \left(x+\frac{\pi}{2}\right)+2 \sin \left(x+\frac{3 \pi}{2}\right)+\sin \left(x+\frac{5 \pi}{2}\right) \) (7) \( \sin \left(\frac{\pi}{2}-x\right)+\cos \left(\frac{3 \pi}{2}-x\right)+\cos \left(x-\frac{\pi}{2}\right)+\cos \left(x-\frac{3 \pi}{2}\right) \)

Question 2 \( x=\frac{\pi}{4} \) is a solution to \( \cos (x)-\sin (x)=0 ? \) True False

Instructions Sketch 2 periods of each function. Label coordinates at key points. \( \begin{array}{l}\text { 1. } f(x)=3 \sin x \\ \begin{array}{ll}\text { 2. } f(x)=-4 \cos x \\ \text { 3. } f(x)=-2 \sin x+3 & \text { can also be written } f(x)=3-2 \sin x \\ \text { 4. } f(x)=\frac{1}{2} \cos x-2 \quad \text { can also be written } f(x)=-2+\frac{1}{2} \cos x\end{array}\end{array} \).

Cho \( \cos x=\frac{1}{2} \). Tính giá trị biểu thức \( P=3 \sin ^{2} x+4 \cos ^{2} x \) ?

5. \( \operatorname{sen} x \cdot \sec x=\tan x \)

5. \( \operatorname{sen} x \cdot \sec x=\tan x \)