Identify the adjacent and opposite sides for angle C.

You're on a roll — 3.1.1 Step 1: Identify the adjacent and opposite sides for angle C. In ABC, with ABC = 90^: The side adjacent to angle C is BC. The side opposite to angle C is AB. Step 2: Write the ratio for C. C = adjacentopposite = (BC)/(AB) The ratio of C is (BC)/(AB). 3.1.2 Step 1: Identify the sides AC and AB relative to an angle. AC is the hypotenuse. AB is the side opposite to angle C. AB is the side adjacent to angle A. Step 2: Determine the trigonometric ratio. For angle C, the ratio (AC)/(AB) is hypotenuseopposite, which is C. (AC)/(AB) = C The trigonometric ratio is C. 3.2.1 Step 1: Use the distance formula for OP. Given point P(-3, -4), the coordinates are x = -3 and y = -4. The length OP (radius r) is calculated as: OP = sqrt(x^2 + y^2) Step 2: Substitute the values and calculate. OP = sqrt((-3)^2 + (-4)^2) OP = sqrt(9 + 16) OP = sqrt(25) OP = 5 The length of OP is 5. 3.2.2 Step 1: Determine the values of and . From P(-3, -4) and OP = 5, we have x = -3, y = -4, and r = 5. = (x)/(r) = (-3)/(5) = (1)/( ) = (r)/(x) = (5)/(-3) = (y)/(r) = (-4)/(5) Step 2: Calculate ^2 . ^2 = ((-4)/(5))^2 = (16)/(25) Step 3: Substitute the values into the expression + ^2 . + ^2 = (5)/(-3) + (16)/(25) + ^2 = -(5)/(3) + (16)/(25) Step 4: Find a common denominator and simplify. The common denominator for 3 and 25 is 75. + ^2 = -(5 × 25)/(3 × 25) + (16 × 3)/(25 × 3) + ^2 = -(125)/(75) + (48)/(75) + ^2 = (-125 + 48)/(75) + ^2 = (-77)/(75) The value of + ^2 is -(77)/(75). 3.3 Step 1: Recall the values of the special angles. 45^ = (1)/( 45^) = (1)/(1/sqrt(2)) = sqrt(2) 90^ = 1 60^ = sqrt(3) Step 2: Substitute these values into the expression. ( 45^)/( 90^ · 60^) = sqrt(2)1 · sqrt(3) Step 3: Simplify the expression. sqrt(2)1 · sqrt(3) = sqrt(2)sqrt(3) To rationalize the denominator, multiply the numerator and denominator by sqrt(3): sqrt(2)sqrt(3) × sqrt(3)sqrt(3) = sqrt(2 × 3)3 = sqrt(6)3 The value of the expression is sqrt(6)3. Send me the next one 📸