{"id":1428,"date":"2026-01-28T18:54:14","date_gmt":"2026-01-28T08:54:14","guid":{"rendered":"https:\/\/archive4ones.com\/2ndstudy\/?p=1428"},"modified":"2026-01-28T18:58:40","modified_gmt":"2026-01-28T08:58:40","slug":"year11-math-3-2-5","status":"publish","type":"post","link":"https:\/\/archive4ones.com\/2ndstudy\/?p=1428","title":{"rendered":"Year11 MATH 3-2-5"},"content":{"rendered":"\n

Trigonometric Functions<\/h2>\n\n\n\n

Unit 2<\/h4>\n\n\n\n

Focus: Radians, unit circle, and graphs.<\/em><\/p>\n\n\n\n

    \n
  1. Convert 120<\/mn>\u2218<\/mo><\/msup>120^\\circ<\/annotation><\/semantics><\/math> to radians (in terms of \u03c0<\/mi>\\pi<\/annotation><\/semantics><\/math>).<\/li>\n\n\n\n
  2. Convert 3<\/mn>\u03c0<\/mi><\/mrow>4<\/mn><\/mfrac>\\frac{3\\pi}{4}<\/annotation><\/semantics><\/math> radians to degrees.<\/li>\n\n\n\n
  3. State the exact value of sin<\/mi>\u2061<\/mo><\/mrow>(<\/mo>\u03c0<\/mi>6<\/mn><\/mfrac>)<\/mo><\/mrow>\\sin(\\frac{\\pi}{6})<\/annotation><\/semantics><\/math>.<\/li>\n\n\n\n
  4. State the exact value of cos<\/mi>\u2061<\/mo><\/mrow>(<\/mo>\u03c0<\/mi>)<\/mo><\/mrow>\\cos(\\pi)<\/annotation><\/semantics><\/math>.<\/li>\n\n\n\n
  5. Find the period of the function y<\/mi>=<\/mo>sin<\/mi>\u2061<\/mo><\/mrow>(<\/mo>2<\/mn>x<\/mi>)<\/mo><\/mrow>y = \\sin(2x)<\/annotation><\/semantics><\/math>.<\/li>\n\n\n\n
  6. Find the amplitude of y<\/mi>=<\/mo>\u2212<\/mo>3<\/mn><\/mspace>cos<\/mi>\u2061<\/mo><\/mrow>(<\/mo>x<\/mi>)<\/mo>+<\/mo>1<\/mn><\/mrow>y = -3\\cos(x) + 1<\/annotation><\/semantics><\/math>.<\/li>\n\n\n\n
  7. Solve sin<\/mi>\u2061<\/mo><\/mrow>(<\/mo>x<\/mi>)<\/mo>=<\/mo>0.5<\/mn><\/mrow>\\sin(x) = 0.5<\/annotation><\/semantics><\/math> for 0<\/mn>\u2264<\/mo>x<\/mi>\u2264<\/mo>2<\/mn>\u03c0<\/mi><\/mrow>0 \\le x \\le 2\\pi<\/annotation><\/semantics><\/math>.<\/li>\n\n\n\n
  8. Use the Pythagorean identity sin<\/mi>2<\/mn><\/msup>\u2061<\/mo><\/mspace>\u03b8<\/mi>+<\/mo>cos<\/mi>2<\/mn><\/msup>\u2061<\/mo><\/mspace>\u03b8<\/mi>=<\/mo>1<\/mn><\/mrow>\\sin^2\\theta + \\cos^2\\theta = 1<\/annotation><\/semantics><\/math> to find cos<\/mi>\u2061<\/mo><\/mspace><\/mrow>\u03b8<\/mi><\/mrow>\\cos\\theta<\/annotation><\/semantics><\/math> if sin<\/mi>\u2061<\/mo><\/mspace><\/mrow>\u03b8<\/mi>=<\/mo>3<\/mn>5<\/mn><\/mfrac><\/mrow>\\sin\\theta = \\frac{3}{5}<\/annotation><\/semantics><\/math> and \u03b8<\/mi>\\theta<\/annotation><\/semantics><\/math> is in the first quadrant.<\/li>\n\n\n\n
  9. Find the vertical shift of y<\/mi>=<\/mo>tan<\/mi>\u2061<\/mo><\/mrow>(<\/mo>x<\/mi>)<\/mo>\u2212<\/mo>4<\/mn><\/mrow>y = \\tan(x) – 4<\/annotation><\/semantics><\/math>.<\/li>\n\n\n\n
  10. What is the value of tan<\/mi>\u2061<\/mo><\/mrow>(<\/mo>\u03c0<\/mi>4<\/mn><\/mfrac>)<\/mo><\/mrow>\\tan(\\frac{\\pi}{4})<\/annotation><\/semantics><\/math>?<\/li>\n<\/ol>\n\n\n\n

    Answers:<\/strong><\/p>\n\n\n\n

      \n
    1. 2<\/mn>\u03c0<\/mi><\/mrow>3<\/mn><\/mfrac>\\frac{2\\pi}{3}<\/annotation><\/semantics><\/math> | 2. 135<\/mn>\u2218<\/mo><\/msup>135^\\circ<\/annotation><\/semantics><\/math> | 3. 0.5<\/mn>0.5<\/annotation><\/semantics><\/math> | 4. \u2212<\/mo>1<\/mn><\/mrow>-1<\/annotation><\/semantics><\/math> | 5. \u03c0<\/mi>\\pi<\/annotation><\/semantics><\/math> | 6. 3 | 7. x<\/mi>=<\/mo>\u03c0<\/mi>6<\/mn><\/mfrac>,<\/mo>5<\/mn>\u03c0<\/mi><\/mrow>6<\/mn><\/mfrac><\/mrow>x = \\frac{\\pi}{6}, \\frac{5\\pi}{6}<\/annotation><\/semantics><\/math> | 8. 4<\/mn>5<\/mn><\/mfrac>\\frac{4}{5}<\/annotation><\/semantics><\/math> | 9. Down 4 units | 10. 1.<\/li>\n<\/ol>\n\n\n\n

      <\/p>\n","protected":false},"excerpt":{"rendered":"

      Trigonometric Functions Unit 2 Focus: Radians, unit circle, and graphs. Answers:<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[8],"tags":[],"class_list":["post-1428","post","type-post","status-publish","format-standard","hentry","category-math"],"_links":{"self":[{"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=\/wp\/v2\/posts\/1428","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1428"}],"version-history":[{"count":5,"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=\/wp\/v2\/posts\/1428\/revisions"}],"predecessor-version":[{"id":1445,"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=\/wp\/v2\/posts\/1428\/revisions\/1445"}],"wp:attachment":[{"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1428"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1428"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1428"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}