When placed next to any angle on a triangle, the theta symbol (θ) represents that missing angle.
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The cosine of theta is adjacent over hypotenuse, given a right triangle, theta not being the 90 degree angle, adjacent not being the hypotenuse, and theta being the angle between adjacent and hypotenuse. In a unit triangle, i.e. in a unit circle circumscribed with radius one, and theta and the center of the circle at the origin, cosine of theta is X.
Theta is just a Greek letter used to denote measurement of angle. Sine is a trigonometric function, i.e., the ratio of the side opposite to the angle theta to the hypotenuse of the triangle. So Sine theta means the value of sine function for angle theta, where theta is any angle.
Suppose triangle ABC is right angled at C. Suppose you are given that the angle at B is theta. Thenif you know the length of AB (the hypotenuse), thenBC = AB*cos(theta) andAC = AB*sin(theta)if you know the length of BC, thenAB = BC/cos(theta) andAC = BC*tan(theta)if you know the length of AC, thenAB= AC/sin(theta) andBC = AC/tan(theta)
SOH CAH TOA is a way of remembering what the functions sin, cos, & tan mean in a right angle triangle. With a triangle with one of the acute angles labelled (theta) the longest side H (Hypotenuse), the side opposite the labelled angle O, and the short side closest to the angle A (Adjacent) SOH ->SIN(Theta)=0/H CAH ->COS(Theta)=A/H TOA ->TAN(Theta)=O/A
If tan theta equals 2, then the sides of the triangle could be -2, -1, and square root of 5 (I used the Pythagorean Theorem to get this). From this, sec theta is negative square root of 5. It is negative because theta is in the third quadrant, where cosine, secant, sine, and cosecant are all negative.