Gr12 Mathematics: Ch 4 Sum Trigonometry

<p>To determine where the function is positive or negative</p> Signup and view all the answers

<p>sin(α + β) = sin α cos β + cos α sin β</p> Signup and view all the answers

<p>cos(α + β) = cos α cos β - sin α sin β</p> Signup and view all the answers

<p>sin(2α) = 2 sin α cos α</p> Signup and view all the answers

<p>To find the restricted values</p> Signup and view all the answers

<p>cos(α - β) = cos α cos β - sin α sin β</p> Signup and view all the answers

<p>An infinite number of angles that satisfy the equation</p> Signup and view all the answers

<p>$\cos(\alpha - \beta) = \cos \alpha \cos \beta + \sin \alpha \sin \beta$</p> Signup and view all the answers

<p>Using the negative angle identity</p> Signup and view all the answers

<p>$\sin(\alpha + \beta) = \sin \alpha \cos \beta + \cos \alpha \sin \beta$</p> Signup and view all the answers

<p>To equate two expressions for KL^2</p> Signup and view all the answers

<p>$\cos(\alpha + \beta) = \cos \alpha \cos \beta - \sin \alpha \sin \beta$</p> Signup and view all the answers

<p>$\sin(\alpha - \beta) = \sin \alpha \cos \beta - \cos \alpha \sin \beta$</p> Signup and view all the answers

<p>To simplify the expression for $\cos(-\beta)$</p> Signup and view all the answers

<p>To express trigonometric functions of a sum or difference in terms of functions of the individual angles</p> Signup and view all the answers

<p>theta = 180^degree - sin^(-1)x + k * 360^degree</p> Signup and view all the answers

<p>All of the above</p> Signup and view all the answers

<p>When no right angle is given, and either two sides and the included angle or three sides are given</p> Signup and view all the answers

<p>h = (d sin alpha)/(sin beta) tan beta</p> Signup and view all the answers

<p>h = (b sin alpha sin theta)/(sin(beta + theta))</p> Signup and view all the answers

<p>theta = tan^(-1)x + k * 180^degree</p> Signup and view all the answers

<p>When no right angle is given, and two sides and an angle (not the included angle) are given</p> Signup and view all the answers

<p>Area = (1/2)ab sin C</p> Signup and view all the answers

<p>theta = cos^(-1)x + k * 360^degree</p> Signup and view all the answers

<p>$\cos \alpha \cos eta + \sin \alpha \sin eta$</p> Signup and view all the answers

<p>$\sin \alpha \cos eta + \cos \alpha \sin eta$</p> Signup and view all the answers

<p>Using the distance formula and cosine rule</p> Signup and view all the answers

<p>To derive the formula for $\cos(\alpha - eta)$</p> Signup and view all the answers

<p>To rewrite the angle as a difference</p> Signup and view all the answers

<p>$\sin \alpha \cos eta - \cos \alpha \sin eta$</p> Signup and view all the answers

<p>To extend trigonometric identities</p> Signup and view all the answers

<p>$\cos(\alpha - eta) = \cos \alpha \cos eta + \sin \alpha \sin eta$</p> Signup and view all the answers

<p>cos(α)cos(β) - sin(α)sin(β)</p> Signup and view all the answers

<p>-1/9</p> Signup and view all the answers

<p>sin(α)cos(β) + cos(α)sin(β)</p> Signup and view all the answers

<p>To determine where the function is positive or negative</p> Signup and view all the answers

<p>3/4</p> Signup and view all the answers

<p>cos(α)cos(β) - sin(α)sin(β)</p> Signup and view all the answers

<p>sqrt(3)/2</p> Signup and view all the answers

<p>Simplify the equation using algebraic methods</p> Signup and view all the answers

<p>-7/25</p> Signup and view all the answers

<p>θ = tan⁻¹x + k ⋅ 180°, where k is an integer</p> Signup and view all the answers

<p>All of the above</p> Signup and view all the answers

<p>When no right angle is given, and either two sides and an angle or two angles and a side are given</p> Signup and view all the answers

<p>h = (b sin α sin θ) / (sin(β + θ))</p> Signup and view all the answers

<p>Area = (1/2)ab sin C</p> Signup and view all the answers

<p>When no right angle is given, and three sides are given</p> Signup and view all the answers

<p>h = (d sin α) / (sin β) tan β</p> Signup and view all the answers

<p>θ = sin⁻¹x + k ⋅ 180° or θ = 180° - sin⁻¹x + k ⋅ 360°</p> Signup and view all the answers

<p>Area = (1/2)ab sin C</p> Signup and view all the answers

<p>Draw a sketch, consider the given information, apply appropriate rules, and calculate the desired quantities</p> Signup and view all the answers

<p>√2/2 - 1/2</p> Signup and view all the answers

<p>8√5/9</p> Signup and view all the answers

<p>√2/2 + 1/2</p> Signup and view all the answers

<p>3/4</p> Signup and view all the answers

<p>√3/2</p> Signup and view all the answers

<p>√2/2 - 1/2</p> Signup and view all the answers

<p>\cos \alpha \cos \beta - \sin \alpha \sin \beta</p> Signup and view all the answers

<p>-7/25</p> Signup and view all the answers

<p>To simplify the expression ((\cos \alpha - \cos \beta)^2 + (\sin \alpha - \sin \beta)^2)</p> Signup and view all the answers

<p>√2 - 1/2</p> Signup and view all the answers

<p>Using the negative angle identity</p> Signup and view all the answers

<p>\frac{-1}{9}</p> Signup and view all the answers

<p>-4/9</p> Signup and view all the answers

<p>\sin \alpha \cos \beta - \cos \alpha \sin \beta</p> Signup and view all the answers

<p>\cos \alpha \cos \beta + \sin \alpha \sin \beta</p> Signup and view all the answers

<p>Applying the sine difference formula</p> Signup and view all the answers

<p>To simplify trigonometric expressions</p> Signup and view all the answers

<p>θ = sin⁻¹(x) + k × 360°</p> Signup and view all the answers

<p>θ = cos⁻¹(x) or θ = 180° - cos⁻¹(x)</p> Signup and view all the answers

<p>Area = (1/2)ab sin(C)</p> Signup and view all the answers

<p>When no right angle is given, and either two sides and an angle or three sides are given.</p> Signup and view all the answers

<p>h = (d sin(α)) / sin(β)</p> Signup and view all the answers

<p>Area = (1/2)ab sin(C)</p> Signup and view all the answers

<p>When no right angle is given, and either two angles and a side or two sides and an angle are given.</p> Signup and view all the answers

<p>h = (b sin(α) sin(θ)) / sin(β + θ)</p> Signup and view all the answers

<p>θ = tan⁻¹(x) + k × 180°</p> Signup and view all the answers

<p>Area = √(s(s-a)(s-b)(s-c))</p> Signup and view all the answers