📏 trigonometry

1. **State the problem:** Given $\cos \theta = -\frac{2}{5}$ and $\sin \theta > 0$, find the quadrant of $\theta$ and the values of $\sin \theta$, $\tan \theta$, $\sec \theta$, $\c

1. **State the problem:** We need to find the quadrant(s) where the angle $\theta$ satisfies the inequalities: $$\cos(\theta) < 0$$

1. **Problem Statement:** Determine the quadrant in which angle $\theta$ lies given the inequalities: $$\sin(\theta) < 0$$

1. **Problem Statement:** Given the terminal side of angle $\theta$ lies on the line $-4x + 3y = 0$ in Quadrant IV, find the values of $\sin \theta$, $\cos \theta$, $\tan \theta$,

1. **Problem Statement:** Given the terminal side of angle $\theta$ lies on the line $-4x + 3y = 0$ in Quadrant IV, find $\sin \theta$, $\cos \theta$, $\tan \theta$, $\sec \theta$,

1. **State the problem:** Given $\cos \theta = \frac{6}{10} = 0.6$ and $\tan \theta < 0$, find the values of $\sin \theta$, $\tan \theta$, $\csc \theta$, $\sec \theta$, and $\cot \

1. **Problem statement:** Given point $P(-15, y)$ with $OP=17$ units and reflex angle $\angle MOP=\alpha$, find: 5.1.1 $y$

1. Problem 15: In triangle $\triangle ABC$, given $a=8$ cm, $b=5$ cm, and angle $C=60^\circ 2'$, find side $c$. 2. Use the Law of Cosines formula: $$c^2 = a^2 + b^2 - 2ab \cos C$$

1. Problem 4: In triangle $\triangle ABC$, given $B=35^\circ$, $C=40^\circ$, and side $a=12$ cm, find side $c$. 2. Use the Law of Sines: $$\frac{a}{\sin A} = \frac{c}{\sin C}$$

1. Problem: Solve $2 \sin \theta - \sqrt{2} = 0$ for $0^\circ \leq \theta \leq 360^\circ$. Formula: $\sin \theta = \frac{\sqrt{2}}{2}$.

1. State the problem. In triangle ABC we are given $b=4.2\,\text{cm}$, $c=7.5\,\text{cm}$ and $A=48^\circ36'$.

1. The problem involves evaluating multiple trigonometric expressions and identities. 2. Recall key trigonometric identities:

1. **Problem Statement:** We have two functions: $f(x) = -2 \cos x$ and $g(x) = \sin 2x$ defined on the interval $-90^\circ \leq x \leq 180^\circ$. We need to:

1. **Stel die probleem:** Ons het twee funksies: $$f(x) = a \sin(bx) + 1$$

1. **Problem:** Find all values of $\theta$ such that $\sin \theta = \frac{1}{2}$ and $0 \leq \theta \leq 2\pi$. 2. **Formula and rules:** The sine function gives the ratio of the

1. **Problem statement:** We have a right triangle with angles 45°, 30°, and 90°, and the base (adjacent to the 45° angle) is 26 cm. We need to find the hypotenuse length $d$. 2. *

1. **Problem Statement:** We are asked to analyze the function $y = \cos x$ for the domain $0^\circ \leq x \leq 360^\circ$.

1. **Problem statement:** We need to find the length of the hypotenuse in a right-angled triangle where one angle is 60° and the side adjacent to this angle is 6 meters. 2. **Formu

1. **Problem Statement:** We are given that angle $x$ is obtuse, meaning $90^\circ < x < 180^\circ$. We need to determine the truth value of the following statements: a) $\sin x >

1. **State the problem:** We need to define the three primary trigonometric ratios in terms of Cartesian coordinates $x$, $y$, and radius $r$.

1. **Problem statement:** Given functions $f(x) = -2\cos x$ and $g(x) = \sin 2x$ for $-90^\circ \leq x \leq 180^\circ$, we need to: - Draw graphs of $f$ and $g$ on the same axes.