📏 trigonometry

1. The problem asks for the phase shift of the function $$y = 4 \cos(x + \pi) - 2$$. 2. The general form of a cosine function with phase shift is $$y = A \cos(B(x - C)) + D$$, wher

1. **State the problem:** Find the period of the function $y = 4 \cos(5x)$.\n\n2. **Recall the formula for the period of cosine:** The general form is $y = A \cos(Bx)$, where the p

1. **State the problem:** We need to find two angles in radians between $-2\pi$ and $2\pi$ whose terminal sides pass through the origin and a given point on the circle in the recta

1. **State the problem:** We need to find the period of the functions $y = \sin(x)$ and $y = \cos(x)$. Both are trigonometric functions with well-known periodic behavior. 2. **Reca

1. **State the problem:** Express $\tan K$ as a fraction in simplest terms given the values related to triangle sides or angles. 2. **Recall the definition:** $\tan K = \frac{\text

1. **Stel het probleem vast:** We hebben punten M'(-0.2, 0.98) en M(\frac{3}{5}, -\frac{4}{5}) op een cirkel met middelpunt O(0,0).

1. **Problem Statement:** Find the missing side length $x$ and the missing angle in a right triangle where side $AC=12$ cm, angle $A=25^\circ$, and side $BC=x$ is unknown.

1. **State the problem:** We have a right triangle with one angle measuring $32^\circ$, one leg measuring 14 units, and the hypotenuse labeled as $x$. We need to find the length of

1. **Stating the problem:** Simplify the expression $$\sin(90^\circ - \alpha) + \tan(54^\circ - \alpha) - \cos(90^\circ - \alpha) + \sin(-\alpha) + \sin(\alpha - 120^\circ) - \tan(

1. **State the problem:** We need to find the distance $x$ between two poles connected by a wire of length 80 ft, where the wire forms a 20° angle with the horizontal. 2. **Identif

1. **State the problem:** We need to find the height of a building given that from a point 12 feet away from its base, the angle of elevation to the top is 70°. 2. **Identify the r

1. **State the problem:** From a point 12 feet from the base of a building, the angle of elevation to the top of the building is 70°. We need to find the height of the building.

1. The problem involves using the SOH CAH TOA mnemonic to solve for $x$ in a right triangle. 2. The given equation is $a \times \tan 62^\circ = \frac{x}{7} \times 9$ and the value

1. **State the problem:** We have a right triangle with an angle of 43° at vertex A, the vertical leg is 7 cm, the horizontal leg is $x$, and the hypotenuse is $h$. We want to find

1. **Problem statement:** Given a triangle ABC with angles $\alpha = 32^\circ$, $\beta = 58^\circ$, and side $c = 15$ cm opposite angle $C$, find side $b$ opposite angle $B$ using

1. **Problem statement:** Find the missing side $x$ in the triangle with given side 14 m opposite angle 65°, and angle opposite $x$ is 44°. 2. **Formula used:** Law of Sines states

1. The problem is to find the value of $\cos 60^\circ$. 2. Recall the cosine function for special angles. The cosine of $60^\circ$ is a well-known value from the unit circle.

1. The problem is to simplify the expression $$\frac{\cos \theta}{2} \pm \frac{5 \sin \theta}{5} \cos 60^\circ$$. 2. Recall that $$\cos 60^\circ = \frac{1}{2}$$.

1. The problem is to find an equation for the sine wave graph shown, which oscillates between approximately -6 and 6 on the y-axis and spans from about -3 to 10 on the x-axis. 2. T

1. **State the problem:** We need to find an equation for the given wave-like graph that resembles a sine or cosine function. 2. **Identify the type of function:** The graph looks

1. **State the problem:** Kayla observes a plane flying at an altitude of 880 m. The angle of elevation changes from 67° 40' to 24° 30' after 25 seconds. We need to find (a) how fa